888 Answered Questions for the topic discrete math

Discrete Math

03/28/22

Is the function f : S → {1,−1} f : [x]∼ ↦ (−1) well defined?

a∼b  ⇔  a and b have the same remainder from division by n. Let n=3, and consider the quotient set S = ℤ/∼ (we of course have that |S| = 3). Is the function f : S → {1,−1}f : [x]∼ ↦ (−1) well... more
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Discrete Math

03/28/22

Define an equivalence relation ~ on S×T
Make the projection π : S×T → S a special case of the projection to a quotient.Specifically, define an equivalence relation ~ on S×T such that the projection π: S×T→(S×T)/∼ coincides with π : S×T →... more
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Discrete Math

03/28/22

Describe an isomorphism between the equivalence class [f]∼ and the set ℝ.
Let S be the set of differentiable functions ℝ→ℝ . Let ∼ be the relation defined on S by f1∼f2  if and only if  ∀x∈ℝ,f′1(x)=f′2(x). Let f∈S be a differentiable function. Describe an isomorphism... more
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Discrete Math Math English Statistics

03/25/22

Having a lot of trouble with this. Can someone help?
A fine dining restaurant claims that the group sizes of their customers follows the following distribution: 2 people3 people4 people4+ people 32% 13% 18% 37% Gustavo, a waiter at the restaurant,... more
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03/20/22

Discreete math functions
Let A, B be sets and f : A → B a function between them. Let also C, D ⊆ A and E, F ⊆ B be subsets. Prove the following. 1. f(C ∩ D) ⊆ f(C) ∩ f(D) 2. f−1(E ∩ F) = f−1(E) ∩ f−1(F)3. f−1(C) \... more
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Discrete Math Math Logic

03/18/22

How to use natural deduction to prove a statement.
Prove the following statement using natural deduction rules (such as conjunction elimination, implication introduction, etc.)[(p ∧ q) ∨ (p ∧ r)] ⊢ [p ∧ (q ∨ r)]
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03/18/22

How to use natural deduction to prove a statement.
Prove the following statements using natural deduction rules (such as conjunction elimination, implication introduction, etc.)a. [(p ∧ q) ∨ (p ∧ r)] ⊢ [p ∧ (q ∨ r)]b. [¬p, p ∨ q] ⊢ [q]c. [¬p ∧ ¬q]... more
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03/14/22

Is function invertible
Prove or disprove: If a, b and c are real numbers where 'a' is not equal to 0, then ax^2 + bx + c is invertible.
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03/14/22

Describe the equivalence class
Let R be the relation on Z × (Z \ {0}) defined by (a, b)R(c, d) if and only if ad = bc. Show that R is an equivalence relation on Z × (Z \ {0}) and describe the equivalence class [(0, 1)]
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03/13/22

Discreete math question
Let R be the relation Z defined by aRb if and only if a^2=b^2. Show that R is an equivalence relation on Z and determine its distinct equivalence classes.
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Discrete Math Discrete Mathematics

03/11/22

Using indirect proof, solve this problem
Show using indirect proof. Note that you will also need to use a case analysis here, once you set up the indirect proof. Don’t forget that even if you’re doing informal proofs, you can appeal to... more
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Discrete Math Discrete Mathematics

03/11/22

Using proof by contradiction for problem
The question is: Show using proof by contradiction that there are no two primes p1 and p2 greater than 2 such that p1 − p2 is odd. Remember that a number k is prime if and only if its only factors... more
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Discrete Math

03/03/22

must be proved using contradiction.
For all integers m and n, if m*n is odd, then m is odd and n is odd. (Hint: you'll need two cases in your proof)
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Discrete Math

03/02/22

Spanning Trees Discrete Math
Given G = ( { a, b, c, d, e, f }, E ) and |E| = 15, how many spanning trees can be formed from G if G is undirected?Answer: _ _ _ _ _
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Discrete Math

03/02/22

Graph Theory Discrete Math
Given G = ( { a, b, c, d, e, f, g, h, i, j }, E ) and |E| = 45, how many different length-6 walks starting from a are there in G if G is undirected?Answer: _ _ _ _ _
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Discrete Math

03/02/22

Graph Theory Discrete Math
Given G = ( { a, b, c, d, e, f, g, h, i, j }, E ) and |E| = 45, how many different length-6 walks are there in G if G is undirected?Answer: _ _ _ _ _ _
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Discrete Math

03/02/22

Permutations Discrete Math
Given A = { n ∈ ℤ : |n| < 7 } and B = ℘(A), how many permutations of the elements in B start with { 1, 2 }?Answer: _ _ _ _ _
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Discrete Math

03/02/22

Given A ⊂ ℤ, |A| = 13, |B| = |C| = 3, and B, C ⊂ A, what is the probability that |C ∖ B| = 0?
Given A ⊂ ℤ, |A| = 13, |B| = |C| = 3, and B, C ⊂ A, what is the probability that |C ∖ B| = 0?Answer: _ _ _ _ _ _ _
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Discrete Math

03/02/22

How many directed graphs have nine vertices and exactly four edges?
How many directed graphs have nine vertices and exactly four edges?Answer: _ _ _ _ _ _ _
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02/25/22

Venn diagram to expression.
How do I make an expression out of this Venn diagram. I know that the intersection between A and B can be described as A ∩ B. But how do I include the universal set. That is, all the gray that is... more
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Discrete Math

02/17/22

discrete math question

prove that 1^2 + 2^2 +...+n^2 = (1/6) n (n+1)(2n+1) if n is an integer >= 1
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Discrete Math

02/17/22

discrete math question

prove that the sum of k C(n,k), 1<=k<=n is n x 2^(n-1)
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Discrete Math

02/17/22

Discrete Math Question
Suppose that there are 13 cards, numbered 1,2,......, 13. A hand is 5 cards, the order in which the cards are dealt not making any difference. How many hands are there? The value of a hand,... more
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Discrete Math

02/17/22

Discrete Math Question

Suppose you are playing 5-card draw poker- the deck has the usual 52 cards and you are dealt 5. What is the chance that you are dealt three aces (but not 4 and not an additional pair)? Suppose you... more
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Discrete Math Discrete Mathematics

02/14/22

Let a, b, c be integers. Prove that ...
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