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Discrete Mathematics Discrete Math

02/07/22

Prove that mn^k is even if k > 0

Let n, m, k be integers where n is even and m is odd. Prove that mn^k is even if k > 0.I know intuitively that n^k can just be expressed as an even number, because n is even. But is that a valid... more

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Discrete Mathematics Discrete Math

02/06/22

Discreete mathematics proof

Let n and m be integers and assume that n is even. Prove that nm is even and that n + m has the same parity as m.

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Discrete Mathematics Math Discrete Math Proofs

01/24/22

There exists a unique integer a such that a + b = b for all integers b.

I am doing this for a proofs class and I keep getting confused about how to prove it

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Discrete Mathematics Discrete Math Finite Math

01/13/22

Thirty points are placed equally spaced on a circle, and the points are labeled with the integers from 1 to 30 in random order.

Prove that no matter what the arrangement of labels is, there are three successive integers whose sum is at least 45.

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Discrete Mathematics Discrete Math

01/02/22

Set Theory: A is a subset of B. Prove that C - B is subset of C - A

A ⊆ B. Prove that C - B ⊆ C - A.My approach:Take element k ∈ C - B. This means that k ∈ C and k ∉ B. Since k ∉ B then k ∉ A because A ⊆ B. It's also true that k ∈ C - A because k ∈ C and k ∉ A.... more

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Discrete Mathematics Discrete Math Probability Expected Number

12/13/21

Expected number of becoming good friends

Consider a group of people. There are 500 people in the a room. If we put them altogether inside a room for 1 hour, each pair of people has a 1 in 10000 chances of making friends together and... more

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Discrete Mathematics

11/30/21

√2 +√3 is irrational (by contradiction proof)

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Discrete Mathematics

11/30/21

The difference of odd and even integer is odd ( direct proof )

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Discrete Mathematics Discrete Math Relations

11/29/21

Relation Math Question

Let R = {(a,b)∣a divides b} be a relation on the set {Z}^+Which of the following statements are correct? Tick all the corresponding answers.a) R ⊆ Z^+ × Z^+b) R is reflexive.c) R is... more

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Discrete Mathematics Calculus Discrete Math

11/24/21

An employee joined a company in 2019 with a starting salary of 120,000 Dhs per year. Every year this employee receives araise of 5% of the salary of the previous year.

a. Set up a recurrence relation for the salary of this employee. (Open formula)b. Find an explicit formula for the salary of this employee n years after 2019. (Closed formula)c. What... more

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Discrete Mathematics Calculus Discrete Math

11/24/21

produces car number plates by choosing a positive integer less than 100,000 followed a category number no exceeding 100.How many different car plates can traffic police produce using these criteria?

I need an answer ASAP PLEASE!

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Discrete Mathematics Calculus Discrete Math

11/24/21

c. A license plate begins with three letters. If the possible letters are A, B, C, D and E, how many different permutations of these letters can be made if no letter is used more than once?

I need an answer ASAP PLEASE!

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Discrete Mathematics Calculus Discrete Math

11/24/21

How many permutations of the letters STUVWXZA contain the strings UVW or ST?

I need an answer to this question ASAP!

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Discrete Mathematics Calculus Discrete Math

11/24/21

How many bit strings of length 15 contain at least three 1s and at least three 0s?

I need an answer to this question ASAP!

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Discrete Mathematics Discrete Math

11/16/21

Proof Maths Help

For the following claimed logical equivalence, determine whether it is true or false. Give a proof if it is true, and give a counterexample if it is false. ∀xP(x)∨∀xQ(x)≡∀x(P(x)∨Q(x))

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Discrete Mathematics

11/15/21

Set relations and set operations

Prove using logical equivalences and valid argument forms.Let U be the Universal set and A,B a subset of UIf A is a subset of B and X is not an element of B, then X is not an element of A

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Discrete Mathematics Math Calculus Discrete Math

11/04/21

word problem question below, please show workings.

A system development project calls for five different tasks to be assigned to Maria, Jon, and Suzanne. In how many ways can the assignment be done if each of the three workers must get at least one... more

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Discrete Mathematics Math Discrete Math

11/04/21

prove that [x] + 1 = [x + 1]

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Discrete Mathematics

10/26/21

Problem discrete math

Let A = {1, 2, . . . , 999}. (a) Find how many numbers in A are not divisible by 3 and 7. (b) Find the number of subsets B ⊆ A such that B ∩ {1, 2, 3, 4} = {1, 2}.

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Discrete Mathematics Discrete Math

10/19/21

Partial Order Relations

Let A = Z. Let R be defined on A × A where xRy if x ≤ y . Prove that R is a partial order relation.

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Discrete Mathematics Geometry Discrete Math

10/17/21

How do you prove Binet's Formula for Fibonacci Numbers using mathematical induction?

The Fibonacci numbers form the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, ...where F1 = 1, F2 = 1, FN = FN-2 + FN-1.Binet's Formula is:FN = ([(1+√5)/2]N - [(-1+√5)/2]N)/√5

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Discrete Mathematics Computer Discrete Math Computer Science

10/08/21