Discrete Mathematics Solved Problems

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Discrete math is very broadly the area of mathematics that deals with discrete objects; that is, objects that be enumerated.

Another very broad description is that branches of mathematics considered discrete math are primarily concerned with sets, whereas branches of math known as analysis (such as calculus) are primarily concerned with functions.

It will immensely help anyone trying to crack an exam or an interview.

Here’s the list of Best Reference Books in Discrete Mathematics.

I am mainly confused and clueless about how x1 x2 = 5 is equal to w1 w2 = 7.

Please explain and show me the steps and formulas and such used to figure this out The key here are the restrictions on $w$'s and $x$'s.$w$'s are integers greater than [[

Please explain and show me the steps and formulas and such used to figure this out The key here are the restrictions on $w$'s and $x$'s.

$w$'s are integers greater than $0$, so they are integers greater than or equal to $1$. The number of solutions of $w_1 w_2=7$, with the restriction $w_1\gt 0$, $w_2\gt 0$ is the number of ways to distribute the $7$ candies between $2$ kids, with each kid getting at least $1$ candy. Now distribute the $5$ remaining candies among the kids, with each kid getting $0$ or more candies.

They just subtracted $1$ from each $w$, and called it $x$. This way you have for the first equation $\binom$ solutions (you choose combinations of two numbers from where you can repeat and those numbers sum 7) and for the second you have the same number of solutions but you choose your two numbers from and this time they must sum 5. The number of ways to do this is the number of solutions of $x_1 x_2=5$, with $x_1\ge 0$, $x_2\ge 0$.

This way of systematic learning will prepare anyone easily towards Discrete Mathematics interviews, online tests, examinations and certifications.

– 1000 Multiple Choice Questions & Answers in Discrete Mathematics with explanations – Every MCQ set focuses on a specific topic in Discrete Mathematics Subject Who should Practice these Discrete Mathematics Questions?

||

Please explain and show me the steps and formulas and such used to figure this out The key here are the restrictions on $w$'s and $x$'s.$w$'s are integers greater than $0$, so they are integers greater than or equal to $1$. The number of solutions of $w_1 w_2=7$, with the restriction $w_1\gt 0$, $w_2\gt 0$ is the number of ways to distribute the $7$ candies between $2$ kids, with each kid getting at least $1$ candy. Now distribute the $5$ remaining candies among the kids, with each kid getting $0$ or more candies.They just subtracted $1$ from each $w$, and called it $x$. This way you have for the first equation $\binom$ solutions (you choose combinations of two numbers from where you can repeat and those numbers sum 7) and for the second you have the same number of solutions but you choose your two numbers from and this time they must sum 5. The number of ways to do this is the number of solutions of $x_1 x_2=5$, with $x_1\ge 0$, $x_2\ge 0$.This way of systematic learning will prepare anyone easily towards Discrete Mathematics interviews, online tests, examinations and certifications.– 1000 Multiple Choice Questions & Answers in Discrete Mathematics with explanations – Every MCQ set focuses on a specific topic in Discrete Mathematics Subject Who should Practice these Discrete Mathematics Questions?Scheduling tasks to be completed by a set of machines is a bin-packing problem, which is part of discrete optimization.Google describes the issue for multiple types of jobs on multiple machines. S., the legislative branch of the government has a House of Representatives with 435 members.These topics are chosen from a collection of most authoritative and best reference books on Discrete Mathematics.One should spend 1 hour daily for 2-3 months to learn and assimilate Discrete Mathematics comprehensively.Types of Set Sets Set Operations – 1 Set Operations – 2 Venn Diagram Algebraic Laws on Sets Cartesian Product of Sets Subsets Functions The Growth of Functions Domain and Range of Functions Number of Functions Floor and Ceiling Function Inverse of a Function Arithmetic Sequences Geometric Sequences Arithmetic and Geometric Mean Special Sequences Harmonic Sequences Cardinality of Sets Types of Matrices Operations on Matrices Properties of Matrices Transpose of Matrices Inverse of Matrices Sequences and Summations Weighed Means The section contains questions on prime numbers, quadratic residue, lcm, hcf, base conversion, exponent rules, number complement, number theory applications, modular exponentiation, ciphers, cryptography encryption and decryption.The section contains questions on counting and pigeonhole principle, linear and circular permutations, combinations, divisors, derangement, recurrence relation, binomial expansion terms and coefficient.

]]$, so they are integers greater than or equal to

Please explain and show me the steps and formulas and such used to figure this out The key here are the restrictions on $w$'s and $x$'s.

$w$'s are integers greater than $0$, so they are integers greater than or equal to $1$. The number of solutions of $w_1 w_2=7$, with the restriction $w_1\gt 0$, $w_2\gt 0$ is the number of ways to distribute the $7$ candies between $2$ kids, with each kid getting at least $1$ candy. Now distribute the $5$ remaining candies among the kids, with each kid getting $0$ or more candies.

They just subtracted $1$ from each $w$, and called it $x$. This way you have for the first equation $\binom$ solutions (you choose combinations of two numbers from where you can repeat and those numbers sum 7) and for the second you have the same number of solutions but you choose your two numbers from and this time they must sum 5. The number of ways to do this is the number of solutions of $x_1 x_2=5$, with $x_1\ge 0$, $x_2\ge 0$.

This way of systematic learning will prepare anyone easily towards Discrete Mathematics interviews, online tests, examinations and certifications.

– 1000 Multiple Choice Questions & Answers in Discrete Mathematics with explanations – Every MCQ set focuses on a specific topic in Discrete Mathematics Subject Who should Practice these Discrete Mathematics Questions?

||

Please explain and show me the steps and formulas and such used to figure this out The key here are the restrictions on $w$'s and $x$'s.$w$'s are integers greater than $0$, so they are integers greater than or equal to $1$. The number of solutions of $w_1 w_2=7$, with the restriction $w_1\gt 0$, $w_2\gt 0$ is the number of ways to distribute the $7$ candies between $2$ kids, with each kid getting at least $1$ candy. Now distribute the $5$ remaining candies among the kids, with each kid getting $0$ or more candies.They just subtracted $1$ from each $w$, and called it $x$. This way you have for the first equation $\binom$ solutions (you choose combinations of two numbers from where you can repeat and those numbers sum 7) and for the second you have the same number of solutions but you choose your two numbers from and this time they must sum 5. The number of ways to do this is the number of solutions of $x_1 x_2=5$, with $x_1\ge 0$, $x_2\ge 0$.This way of systematic learning will prepare anyone easily towards Discrete Mathematics interviews, online tests, examinations and certifications.– 1000 Multiple Choice Questions & Answers in Discrete Mathematics with explanations – Every MCQ set focuses on a specific topic in Discrete Mathematics Subject Who should Practice these Discrete Mathematics Questions?Scheduling tasks to be completed by a set of machines is a bin-packing problem, which is part of discrete optimization.Google describes the issue for multiple types of jobs on multiple machines. S., the legislative branch of the government has a House of Representatives with 435 members.These topics are chosen from a collection of most authoritative and best reference books on Discrete Mathematics.One should spend 1 hour daily for 2-3 months to learn and assimilate Discrete Mathematics comprehensively.Types of Set Sets Set Operations – 1 Set Operations – 2 Venn Diagram Algebraic Laws on Sets Cartesian Product of Sets Subsets Functions The Growth of Functions Domain and Range of Functions Number of Functions Floor and Ceiling Function Inverse of a Function Arithmetic Sequences Geometric Sequences Arithmetic and Geometric Mean Special Sequences Harmonic Sequences Cardinality of Sets Types of Matrices Operations on Matrices Properties of Matrices Transpose of Matrices Inverse of Matrices Sequences and Summations Weighed Means The section contains questions on prime numbers, quadratic residue, lcm, hcf, base conversion, exponent rules, number complement, number theory applications, modular exponentiation, ciphers, cryptography encryption and decryption.The section contains questions on counting and pigeonhole principle, linear and circular permutations, combinations, divisors, derangement, recurrence relation, binomial expansion terms and coefficient.

$. The number of solutions of $w_1 w_2=7$, with the restriction $w_1\gt 0$, $w_2\gt 0$ is the number of ways to distribute the $ candies between $ kids, with each kid getting at least

Please explain and show me the steps and formulas and such used to figure this out The key here are the restrictions on $w$'s and $x$'s.

$w$'s are integers greater than $0$, so they are integers greater than or equal to $1$. The number of solutions of $w_1 w_2=7$, with the restriction $w_1\gt 0$, $w_2\gt 0$ is the number of ways to distribute the $7$ candies between $2$ kids, with each kid getting at least $1$ candy. Now distribute the $5$ remaining candies among the kids, with each kid getting $0$ or more candies.

They just subtracted $1$ from each $w$, and called it $x$. This way you have for the first equation $\binom$ solutions (you choose combinations of two numbers from where you can repeat and those numbers sum 7) and for the second you have the same number of solutions but you choose your two numbers from and this time they must sum 5. The number of ways to do this is the number of solutions of $x_1 x_2=5$, with $x_1\ge 0$, $x_2\ge 0$.

This way of systematic learning will prepare anyone easily towards Discrete Mathematics interviews, online tests, examinations and certifications.

– 1000 Multiple Choice Questions & Answers in Discrete Mathematics with explanations – Every MCQ set focuses on a specific topic in Discrete Mathematics Subject Who should Practice these Discrete Mathematics Questions?

||

Please explain and show me the steps and formulas and such used to figure this out The key here are the restrictions on $w$'s and $x$'s.$w$'s are integers greater than $0$, so they are integers greater than or equal to $1$. The number of solutions of $w_1 w_2=7$, with the restriction $w_1\gt 0$, $w_2\gt 0$ is the number of ways to distribute the $7$ candies between $2$ kids, with each kid getting at least $1$ candy. Now distribute the $5$ remaining candies among the kids, with each kid getting $0$ or more candies.They just subtracted $1$ from each $w$, and called it $x$. This way you have for the first equation $\binom$ solutions (you choose combinations of two numbers from where you can repeat and those numbers sum 7) and for the second you have the same number of solutions but you choose your two numbers from and this time they must sum 5. The number of ways to do this is the number of solutions of $x_1 x_2=5$, with $x_1\ge 0$, $x_2\ge 0$.This way of systematic learning will prepare anyone easily towards Discrete Mathematics interviews, online tests, examinations and certifications.– 1000 Multiple Choice Questions & Answers in Discrete Mathematics with explanations – Every MCQ set focuses on a specific topic in Discrete Mathematics Subject Who should Practice these Discrete Mathematics Questions?Scheduling tasks to be completed by a set of machines is a bin-packing problem, which is part of discrete optimization.Google describes the issue for multiple types of jobs on multiple machines. S., the legislative branch of the government has a House of Representatives with 435 members.These topics are chosen from a collection of most authoritative and best reference books on Discrete Mathematics.One should spend 1 hour daily for 2-3 months to learn and assimilate Discrete Mathematics comprehensively.Types of Set Sets Set Operations – 1 Set Operations – 2 Venn Diagram Algebraic Laws on Sets Cartesian Product of Sets Subsets Functions The Growth of Functions Domain and Range of Functions Number of Functions Floor and Ceiling Function Inverse of a Function Arithmetic Sequences Geometric Sequences Arithmetic and Geometric Mean Special Sequences Harmonic Sequences Cardinality of Sets Types of Matrices Operations on Matrices Properties of Matrices Transpose of Matrices Inverse of Matrices Sequences and Summations Weighed Means The section contains questions on prime numbers, quadratic residue, lcm, hcf, base conversion, exponent rules, number complement, number theory applications, modular exponentiation, ciphers, cryptography encryption and decryption.The section contains questions on counting and pigeonhole principle, linear and circular permutations, combinations, divisors, derangement, recurrence relation, binomial expansion terms and coefficient.

$ candy. Now distribute the $ remaining candies among the kids, with each kid getting [[

Please explain and show me the steps and formulas and such used to figure this out The key here are the restrictions on $w$'s and $x$'s.

$w$'s are integers greater than $0$, so they are integers greater than or equal to $1$. The number of solutions of $w_1 w_2=7$, with the restriction $w_1\gt 0$, $w_2\gt 0$ is the number of ways to distribute the $7$ candies between $2$ kids, with each kid getting at least $1$ candy. Now distribute the $5$ remaining candies among the kids, with each kid getting $0$ or more candies.

They just subtracted $1$ from each $w$, and called it $x$. This way you have for the first equation $\binom$ solutions (you choose combinations of two numbers from where you can repeat and those numbers sum 7) and for the second you have the same number of solutions but you choose your two numbers from and this time they must sum 5. The number of ways to do this is the number of solutions of $x_1 x_2=5$, with $x_1\ge 0$, $x_2\ge 0$.

This way of systematic learning will prepare anyone easily towards Discrete Mathematics interviews, online tests, examinations and certifications.

– 1000 Multiple Choice Questions & Answers in Discrete Mathematics with explanations – Every MCQ set focuses on a specific topic in Discrete Mathematics Subject Who should Practice these Discrete Mathematics Questions?

||

Please explain and show me the steps and formulas and such used to figure this out The key here are the restrictions on $w$'s and $x$'s.$w$'s are integers greater than $0$, so they are integers greater than or equal to $1$. The number of solutions of $w_1 w_2=7$, with the restriction $w_1\gt 0$, $w_2\gt 0$ is the number of ways to distribute the $7$ candies between $2$ kids, with each kid getting at least $1$ candy. Now distribute the $5$ remaining candies among the kids, with each kid getting $0$ or more candies.They just subtracted $1$ from each $w$, and called it $x$. This way you have for the first equation $\binom$ solutions (you choose combinations of two numbers from where you can repeat and those numbers sum 7) and for the second you have the same number of solutions but you choose your two numbers from and this time they must sum 5. The number of ways to do this is the number of solutions of $x_1 x_2=5$, with $x_1\ge 0$, $x_2\ge 0$.This way of systematic learning will prepare anyone easily towards Discrete Mathematics interviews, online tests, examinations and certifications.– 1000 Multiple Choice Questions & Answers in Discrete Mathematics with explanations – Every MCQ set focuses on a specific topic in Discrete Mathematics Subject Who should Practice these Discrete Mathematics Questions?Scheduling tasks to be completed by a set of machines is a bin-packing problem, which is part of discrete optimization.Google describes the issue for multiple types of jobs on multiple machines. S., the legislative branch of the government has a House of Representatives with 435 members.These topics are chosen from a collection of most authoritative and best reference books on Discrete Mathematics.One should spend 1 hour daily for 2-3 months to learn and assimilate Discrete Mathematics comprehensively.Types of Set Sets Set Operations – 1 Set Operations – 2 Venn Diagram Algebraic Laws on Sets Cartesian Product of Sets Subsets Functions The Growth of Functions Domain and Range of Functions Number of Functions Floor and Ceiling Function Inverse of a Function Arithmetic Sequences Geometric Sequences Arithmetic and Geometric Mean Special Sequences Harmonic Sequences Cardinality of Sets Types of Matrices Operations on Matrices Properties of Matrices Transpose of Matrices Inverse of Matrices Sequences and Summations Weighed Means The section contains questions on prime numbers, quadratic residue, lcm, hcf, base conversion, exponent rules, number complement, number theory applications, modular exponentiation, ciphers, cryptography encryption and decryption.The section contains questions on counting and pigeonhole principle, linear and circular permutations, combinations, divisors, derangement, recurrence relation, binomial expansion terms and coefficient.

]]$ or more candies.They just subtracted

Please explain and show me the steps and formulas and such used to figure this out The key here are the restrictions on $w$'s and $x$'s.

$w$'s are integers greater than $0$, so they are integers greater than or equal to $1$. The number of solutions of $w_1 w_2=7$, with the restriction $w_1\gt 0$, $w_2\gt 0$ is the number of ways to distribute the $7$ candies between $2$ kids, with each kid getting at least $1$ candy. Now distribute the $5$ remaining candies among the kids, with each kid getting $0$ or more candies.

They just subtracted $1$ from each $w$, and called it $x$. This way you have for the first equation $\binom$ solutions (you choose combinations of two numbers from where you can repeat and those numbers sum 7) and for the second you have the same number of solutions but you choose your two numbers from and this time they must sum 5. The number of ways to do this is the number of solutions of $x_1 x_2=5$, with $x_1\ge 0$, $x_2\ge 0$.

This way of systematic learning will prepare anyone easily towards Discrete Mathematics interviews, online tests, examinations and certifications.

– 1000 Multiple Choice Questions & Answers in Discrete Mathematics with explanations – Every MCQ set focuses on a specific topic in Discrete Mathematics Subject Who should Practice these Discrete Mathematics Questions?

||

Please explain and show me the steps and formulas and such used to figure this out The key here are the restrictions on $w$'s and $x$'s.$w$'s are integers greater than $0$, so they are integers greater than or equal to $1$. The number of solutions of $w_1 w_2=7$, with the restriction $w_1\gt 0$, $w_2\gt 0$ is the number of ways to distribute the $7$ candies between $2$ kids, with each kid getting at least $1$ candy. Now distribute the $5$ remaining candies among the kids, with each kid getting $0$ or more candies.They just subtracted $1$ from each $w$, and called it $x$. This way you have for the first equation $\binom$ solutions (you choose combinations of two numbers from where you can repeat and those numbers sum 7) and for the second you have the same number of solutions but you choose your two numbers from and this time they must sum 5. The number of ways to do this is the number of solutions of $x_1 x_2=5$, with $x_1\ge 0$, $x_2\ge 0$.This way of systematic learning will prepare anyone easily towards Discrete Mathematics interviews, online tests, examinations and certifications.– 1000 Multiple Choice Questions & Answers in Discrete Mathematics with explanations – Every MCQ set focuses on a specific topic in Discrete Mathematics Subject Who should Practice these Discrete Mathematics Questions?Scheduling tasks to be completed by a set of machines is a bin-packing problem, which is part of discrete optimization.Google describes the issue for multiple types of jobs on multiple machines. S., the legislative branch of the government has a House of Representatives with 435 members.These topics are chosen from a collection of most authoritative and best reference books on Discrete Mathematics.One should spend 1 hour daily for 2-3 months to learn and assimilate Discrete Mathematics comprehensively.Types of Set Sets Set Operations – 1 Set Operations – 2 Venn Diagram Algebraic Laws on Sets Cartesian Product of Sets Subsets Functions The Growth of Functions Domain and Range of Functions Number of Functions Floor and Ceiling Function Inverse of a Function Arithmetic Sequences Geometric Sequences Arithmetic and Geometric Mean Special Sequences Harmonic Sequences Cardinality of Sets Types of Matrices Operations on Matrices Properties of Matrices Transpose of Matrices Inverse of Matrices Sequences and Summations Weighed Means The section contains questions on prime numbers, quadratic residue, lcm, hcf, base conversion, exponent rules, number complement, number theory applications, modular exponentiation, ciphers, cryptography encryption and decryption.The section contains questions on counting and pigeonhole principle, linear and circular permutations, combinations, divisors, derangement, recurrence relation, binomial expansion terms and coefficient.

$ from each $w$, and called it $x$. This way you have for the first equation $\binom$ solutions (you choose combinations of two numbers from where you can repeat and those numbers sum 7) and for the second you have the same number of solutions but you choose your two numbers from and this time they must sum 5. The number of ways to do this is the number of solutions of $x_1 x_2=5$, with $x_1\ge 0$, $x_2\ge 0$.This way of systematic learning will prepare anyone easily towards Discrete Mathematics interviews, online tests, examinations and certifications.– 1000 Multiple Choice Questions & Answers in Discrete Mathematics with explanations – Every MCQ set focuses on a specific topic in Discrete Mathematics Subject Who should Practice these Discrete Mathematics Questions?Scheduling tasks to be completed by a set of machines is a bin-packing problem, which is part of discrete optimization.Google describes the issue for multiple types of jobs on multiple machines. S., the legislative branch of the government has a House of Representatives with 435 members.These topics are chosen from a collection of most authoritative and best reference books on Discrete Mathematics.One should spend 1 hour daily for 2-3 months to learn and assimilate Discrete Mathematics comprehensively.Types of Set Sets Set Operations – 1 Set Operations – 2 Venn Diagram Algebraic Laws on Sets Cartesian Product of Sets Subsets Functions The Growth of Functions Domain and Range of Functions Number of Functions Floor and Ceiling Function Inverse of a Function Arithmetic Sequences Geometric Sequences Arithmetic and Geometric Mean Special Sequences Harmonic Sequences Cardinality of Sets Types of Matrices Operations on Matrices Properties of Matrices Transpose of Matrices Inverse of Matrices Sequences and Summations Weighed Means The section contains questions on prime numbers, quadratic residue, lcm, hcf, base conversion, exponent rules, number complement, number theory applications, modular exponentiation, ciphers, cryptography encryption and decryption.The section contains questions on counting and pigeonhole principle, linear and circular permutations, combinations, divisors, derangement, recurrence relation, binomial expansion terms and coefficient.

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