THK M4 Topic 2 Review 1 Sept. 13

Topic 2 Review 1

​

Multiple Choice

Which of the following is logically equivalent to ~[~p → q]?

• p ∨ ~q

• ~p ∧ q

• ~p ∨ ~q

• ~p ∧ ~q

Multiple Choice

The logically equivalent statement of p → q is ______ .

• ~p ∨ q

• q → ~p

• ~q ∨ p

• ~q ∨ ~p

Multiple Choice

The logically equivalent statement of ~p ∨ ~q is _______ .

• ~p ∧ ~q

• ~(p ∧ q)

• ~(p ∨ q)

• p ∧ q

Multiple Choice

Which of the following propositions is true?

• p → q ≡ ~p → ~q

• ~(p → ~q) ≡ ~p ∧ q

• ~(p ⇔ q) ≡ (~ (p → q) ∧ ~ (q → p))

• ~(~p → ~q) ≡ ~p ∧ q

Multiple Choice

What is the contrapositive of the statement “If n is a natural number, then n is an integer.”?

• If n is not a natural number, then n is not an integer.

• If n is an integer, then n is a natural number.

• If n is not an integer, then n is not a natural number.

Multiple Choice

The negation of the statement: Plants take in carbon dioxide and plants give out oxygen.

• Plants do not take in carbon dioxide and plants do not give out oxygen.

• Plants do not take in carbon dioxide or plants do not give out oxygen.

• If plants do not take in carbon dioxide then plants do not give out oxygen.

• Plants do not take in carbon dioxide and plants give out oxygen.

Multiple Choice

The negation of the statement: “101 is not a multiple of 3” is _________ .

• 101 is a multiple of 3.

• 101 is a multiple of 2.

• 101 is an odd number.

• 101 is an even number.

Multiple Select

Which pair of statements have the same meaning?

i.If sun is shining, then sky is filled with clouds.

ii.If sky is filled with clouds, then the sun is shining.

iii.If sky is not filled with clouds, then the sun is not shining.

iv.If sun is not shining, then sky is not filled with clouds.

• Statement I and II have the same meaning.

• Statement I and III have the same meaning.

• Statement I and IV have the same meaning.

• Statement II and III have the same meaning.

• Statement II and IV have the same meaning.

Multiple Choice

The function ((p ∨ (r ∨ q)) ∧ ~(~q ∧ ~r) is equal to the function ______ .

• q ∨ r

• ((p ∨ r) ∨ q)) ∧ (p ∨ r)

• (p ∧ q) ∨ (p ∧ r)

• (p ∨ q) ∧ ~(p ∨ r)

• (p ∧ r) ∨ (p ∧ q)