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Discrete Math Logic

03/08/21

Method of Formal Proofs

People are happy if and only if they are compassionate. Nobody is both happy and compassionate. Hence people are both unhappy and uncompassionate.I need to provide formal proofs of the validity of... more

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Discrete Math Logic

03/06/21

Let A = {−5, −4, −3, −2, −1, 0, 1, 2, 3} and define a relation R on A as follows: For all m, n ∈ A, m R n ⇔ 5|(m^2 − n^2). It is a fact that R is an equivalence relation on A.

Requirements:Use set-roster notation to list the distinct equivalence classes of R. Enter your answer as a comma-separated list of sets.

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Discrete Math Logic Proofs

03/05/21

Find the least non-negative integer that satisfies this existence theorem:

Find the least non-negative integer that satisfies this existence theorem: There exists n is an element of Z (real number) 2n^2 - 7n + 2is prime.

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Discrete Math Computer Science

03/04/21

Graphs- Computer Science

What is the number of connected components in the graph specified by the following adjacency matrix representation? 0 1 1 0 0 0 01 0 1 0 0 0 01 1 0 0 0 0 00 0 0 0 1 0 00 0 0 1 0 1 10 0 0 0 1 0 10 0... more

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Discrete Math Computer Science

03/01/21

Greedy Algorithm

No complicated code: English is the best way to express an algorithm combined with some simple pseudocode when needed. We want to purchase an item of price M and for that we have an... more

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Discrete Math Math Linear Algebra Mathematics

02/27/21

Prove or disprove: A^2 - B^2 = (A - B)(A + B) for all square matrices A and B of the same size.

Prove or disprove: A2 - B2 = (A - B)(A + B) for all square matrices A and B of the same size.

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Discrete Math Calculus Calc Discrete Mathematics

02/26/21

Summations that are functions of n

How do I calculate this with i being n/4 nf(n) = ∑ (i) i=n/4

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Discrete Math Calculus Calc Discrete Mathematics

02/26/21

Summations that are functions of n

I can't figure out how to compute the closed-form sum for this, I'm not sure which rule applies to this, and with i not at 1 or 0. log(n)f(n) = ∑ (5n) i=3

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Discrete Math Math Mathematica Mathematics

02/18/21

Find the least positive int m

such that 2 * 35 * 53 * 23 * m is a perfect square.

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Discrete Math

02/15/21

Discrete Mathematics

How do I get the solution to...Let A={-1,0,2,4,7}. Find f(A) if ?a) f(x)=1b) f(x)= 2x+1c) f(x)=[x/5]d) f(x)=[(x^2+1)/3]

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Discrete Math Math Mathematica Mathematics

02/13/21

Validity of the conclusion using logic rules

a) u V wb) ~wc) q →sd) u → ~pe) ~p → (r ^ ~s)∴ ~q

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Discrete Math Math Mathematica Mathematics

02/13/21

Two column proof and logic laws

((~d V e) ^ (~d V ~e)) -> f ≡ d V f

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Discrete Math Math Mathematica Mathematics

02/13/21

Validity of the conclusion using logic rules

a) u V wb) ~wc) q →sd) u → ~pe) ~p → (r ^ ~s)∴ ~q

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Discrete Math Math Mathematica Mathematics

02/13/21

Two column proof and logic laws

((~d V e) ^ (~d V ~e)) -> f ≡ d V f

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Discrete Math

02/13/21

discrete maths direct proof

16. Prove that if a and b are positive integers, then a/b + b/a ≥ 2.

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Discrete Math

02/12/21

Use iteration to guess an explicit formula for the sequence and use mathematical induction to verify the formula obtained:

Pk = Pk-1 + 2 * 3k, for each integer K ≥ 2, where Pk = 2

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Discrete Math

02/11/21

I. Use mathematical induction, a basis proof, a inductive hypothesis and step to solve:

∀n ∈ N, ∑n i=1 i!(i2 + 1) = (n + 1)!n.II. Give a recursive definition for the set of all strings of 0's and 1's for which all the 0s follow all the 1s.

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Discrete Math Discrete Mathematics

02/09/21

Use laws of logical equivalence to simplify the circuit. Justify each step. ((𝑃 ∧ ~𝑄) ∨ (𝑃 ∧ 𝑄)) ∧ Q

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Discrete Math Discrete Mathematics

02/09/21

Write the statements formally using quantifiers and variables. Make them conditional.

Write the statements formally using quantifiers and variables. Make them conditional. a) A sufficient condition for an integer to be divisible by 8 is that it be divisible by 16. b) If a product... more

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Discrete Math

02/04/21

Given a set (in Description below), what are the range and domain of g?

Let X be the set {1, 2, 5, 6, 7} and Y be the set {7, 3, 9, 8, 6}. Unary function f : X→Y Binary function g : X ×Y →YWhat are the range and domain of g?

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Discrete Math Math Discrete Mathematics

02/04/21

If A is a countable set, how can i show that A has countably many finite subsets?

Lets say that A is a countable set. How would I go about showing that A has countably many finite subsets? I need to show that for every n ∈ N, the set Pn(A) of finite subsets - with exactly n... more

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Discrete Math

01/28/21

Find a7 if a1=-7 and d=5

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Discrete Math Discrete Mathematics

01/26/21

Use laws of logical equivalence to verify the logical equivalence for the statements

Use laws of logical equivalence to verify the logical equivalence for the statements. (do not use truth tables!) Justify each step:𝑝 → 𝑞 ∨ 𝑟 ≡ 𝑝 ∧ ~𝑞 → rPlease show me every step and explain it so... more

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Discrete Math Discrete Mathematics

01/26/21

negation of the following compounded statement:

Write the negation of the following compounded statement: 𝑥 ≤ 20 or 𝑥 > 30 (where 𝑥 is some real number). −1 < 𝑥 ≤ 9

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Discrete Math

01/25/21

Prove that the algorithm shown above for computing n! when n is a non-negative integer is correct.

procedure factorial(n: nonnegative integer)if n=0 then return 1else return n . factorial(n-1){output is n!}

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Method of Formal Proofs

Let A = {−5, −4, −3, −2, −1, 0, 1, 2, 3} and define a relation R on A as follows: For all m, n ∈ A, m R n ⇔ 5|(m^2 − n^2). It is a fact that R is an equivalence relation on A.

Find the least non-negative integer that satisfies this existence theorem:

Graphs- Computer Science

Greedy Algorithm

Prove or disprove: A^2 - B^2 = (A - B)(A + B) for all square matrices A and B of the same size.

Summations that are functions of n

Summations that are functions of n

Find the least positive int m

Discrete Mathematics

Validity of the conclusion using logic rules

Two column proof and logic laws

Validity of the conclusion using logic rules

Two column proof and logic laws

discrete maths direct proof

Use iteration to guess an explicit formula for the sequence and use mathematical induction to verify the formula obtained:

I. Use mathematical induction, a basis proof, a inductive hypothesis and step to solve:

Use laws of logical equivalence to simplify the circuit. Justify each step. ((𝑃 ∧ ~𝑄) ∨ (𝑃 ∧ 𝑄)) ∧ Q

Write the statements formally using quantifiers and variables. Make them conditional.

Given a set (in Description below), what are the range and domain of g?

If A is a countable set, how can i show that A has countably many finite subsets?

Find a7 if a1=-7 and d=5

Use laws of logical equivalence to verify the logical equivalence for the statements

negation of the following compounded statement:

Prove that the algorithm shown above for computing n! when n is a non-negative integer is correct.

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