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...
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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...
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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...
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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...
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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...
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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
10/29/20
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.
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!)...
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Discrete Math Principle Of Mathematical Induction
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....
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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....
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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...
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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
10/23/20
Define x0, x1, x2, ... as follows (in Description). Find the limit of xn as n → ∞. (Assume that the limit exists.)
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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