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Elementary Mathematics: Laws of Logic

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Questions and Answers

Which law is used to rewrite the statement ~p ∨ q → r ∨ ~q?

Commutative law of ∧

Associative law of ∨

Implication law (correct)

De Morgan's law

What is the equivalent form of p→q using De Morgan's law?

~p ∨ q

p ∧ ~q

~(p ∧ ~q) (correct)

p ∨ ~q

Which of the following is a tautology?

p → ~(p→q)

~(p→q) → p (correct)

~(p→q) ∧ p

p ∧ ~(p→q)

If p→q is false, what is the truth value of ~p → q?

True Signup and view all the answers

What is the equivalent form of (p→r)↔(q →r)?

(~p ∨ r)↔(~q ∨ r) Signup and view all the answers

What is the equivalent form of p→q using the implication law?

~p ∨ q Signup and view all the answers

If p→q is false, what is the truth value of p ∨ q?

True Signup and view all the answers

What is the equivalent form of ~(p→q) using the implication law?

p ∧ ~q Signup and view all the answers

What is the equivalent form of (p→r)↔(q →r) using the implication law?

(~p ∨ r)↔(~q ∨ r) Signup and view all the answers

Is the argument 'An interesting teacher keeps me awake. I stay awake in Discrete Mathematics class. Therefore, my Discrete Mathematics teacher is interesting.' valid?

No Signup and view all the answers