888 Answered Questions for the topic discrete math

Discrete Math Discrete Mathematics

11/01/20

forming statements

 a) Choose two simple English propositions and form a conditional statement from them using “only if”.b) Write the inverse, converse and contrapositive of your conditional statement.c) Write the... more
Discrete Math

10/29/20

What is the correct answer to the following blanks to prove that 𝒫(A) ∩ 𝒫(B) ⊆ 𝒫(A ∩ B)?

Suppose A and B are any sets. Let X be any element in 𝒫(A) ∩ 𝒫(B). Then X ∈ 𝒫(A) and X ∈ 𝒫(B) by definition of intersection Hence, X ⊆ A and X ⊆ B by definition of power set So, _____ by... more
Discrete Math

10/29/20

What is the correct answer to the following blanks to prove that 𝒫(A ∩ B) ⊆ 𝒫(A) ∩ 𝒫(B)?

Suppose A and B are any sets. Let X be any element in 𝒫(A ∩ B). Then X⊆A ∩ B by definition of power set So, _____ by definition of subset Thus, _____ by definition of intersection _____ by... more
Discrete Math

10/29/20

Prove the following statement. Assume that all sets are subsets of a universal set U. For all sets A and B, 𝒫(A ∩ B) = 𝒫(A) ∩ 𝒫(B).

Question 1: Proof that 𝒫(A ∩ B) ⊆ 𝒫(A) ∩ 𝒫(B).Question 2: Proof that 𝒫(A) ∩ 𝒫(B) ⊆ 𝒫(A ∩ B).
Discrete Math

10/29/20

What is the correct answer to the Problem in Description below?

Prove the following statement. Assume that all sets are subsets of a universal set U.For all sets A and B, if Ac ⊆ B then A ∪ B = U.Hint: Once you have assumed that A and B are any sets... more
Discrete Math

10/29/20

What is the correct answer to the blanks to show that P(k+1) is true?

Fill in the blanks in the following proof, which shows that the sequence defined by the recurrence relation fk  =  fk − 1 + 2k for each integer k ≥ 2 f1  =  1 satisfies the following... more
Discrete Math

10/29/20

What is the correct answer to the blank to show that P(1) is true?

Fill in the blanks in the following proof, which shows that the sequence defined by the recurrence relation fk  =  fk − 1 + 2k for each integer k ≥ 2 f1  =  1 satisfies the following... more

I am really stumped on answering this Discrete Mathematics Question

Let U={0,1,2,3,...,19}. Select the bit-string that represents the subset {1,3,5,7,11,13,17,19}, using the convention that the right-most bit represents the element 19. 
Discrete Math Math Discrete Mathematics

10/27/20

Discrete mathematics problem concerning tiling with 3 sub questions.

4. Let Tn be the number of ways of tiling a 2 × n rectangle using tiles of dimensions 1 × 2 or 2 × 2. For example, the picture below shows one of the tilings counted by T12. (i) Find (and justify!)... more

10/27/20

Use the Principle of Mathematical Induction to prove that

Use the Principle of Mathematical Induction to prove that 1 + 2^n≤ 3 ^n ∀𝑛 ≥ 1
Discrete Math

10/26/20

Consider the following statement. For all sets A and B, (A ∪ Bc) − B = (A − B) ∪ Bc.

An algebraic proof for the statement should cite a property from Theorem 6.2.2 for every step, but some reasons are missing from the proposed proof below. Indicate which reasons are missing.... more
Discrete Math

10/26/20

Find a counterexample to show that the statement is false. Assume all sets are subsets of a universal set U = {1, 2, 3, 4, 5}.

For all sets A, B, and C,A ∪ (B − C) = (A ∪ B) − (A ∪ C).A, B, C = _____
Discrete Math

10/26/20

Consider the following statement. For all sets A, B, and C, if B ∪ C ⊆ A then (A − B) ∩ (A − C) = ∅.

Let the universal set U be {1, 2, 3, 4, 5}, and assume that all sets are subsets of U. Is the statement true or false? Find subsets of {1, 2, 3, 4, 5} that can be used to answer this question.... more
Discrete Math

10/26/20

Consider the following statement. For all sets A and B, Ac ∪ Bc ⊆ (A ∪ B)c. Identify the error(s) in the proposed proof. (Select all that apply.)

The following is a proposed proof for the statement. Suppose A and B are any sets, such that x ∈ Ac ∪ Bc. Then x ∈ Ac or x ∈ Bc by definition of union. It follows that x ∉ A or x ∉ B by... more

10/23/20

discrete math- pseudo code

Given an integer n show that you can multiply n by 35 using only five multiplications by 2, two additions and storing intermediate results in memory.
Discrete Math

10/23/20

Given a set in Description below, answer the following questions.

Is A ⊆ B? Is B ⊆ A? Is either A or B a proper subset of the other?
Discrete Math

10/23/20

Given a set in Description below, answer the following questions.

Is A ⊆ B? Is B ⊆ A? Is either A or B a proper subset of the other?
Discrete Math

10/23/20

Given a set in Description below, answer the following questions.

Is A ⊆ B? Is B ⊆ A? Is either A or B a proper subset of the other?
Discrete Math

10/23/20

Given a set in Description below, answer the following questions.

Is A ⊆ B? Is B ⊆ A? Is either A or B a proper subset of the other?
Discrete Math Math Discrete Mathematics

10/23/20

Please help me decode this Caesar cipher code LT YT UFWNX

Discrete Math

10/23/20

Find the first four terms of the following recursively defined sequence.

Discrete Math

10/23/20

Find the first four terms of the following recursively defined sequence.

Discrete Math

10/23/20

Find the first four terms of the following recursively defined sequence.

10/21/20

Set Theory and Lists

If A = {b, {b}, ∅} how would we use list notation to write {B: B ⊆ A and B ≠ ∅} If you could explain what I need to do to solve this that would be much appreciated.

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