Question

p: It is Labor Day q: I go to the park. r: I have a picnic with my family. Translate the following statement and determine its truth value. ~p -> (~q ^ r) A. If it is not Labor Day, then I will go to the park and have a picnic with my family. True B. If it is not Labor Day, then I will go to the park and have a picnic with my family. False C. If it is not Labor Day, then I will not go to the park and have a picnic with my family. False D. If it is not Labor Day, then I will not go to the park and have a picnic with my family. True

Answer 1

I think the correct answer is B. Its definitely not A or D

Answer 2

Option C. is the answer.

Explanation:

Given statements p, q and r are

p: It is a labor day - Truth value (True)

q: I go to the park - Truth value (True)

r: I have a picnic with my family - Truth value (True)

Now we will find the truth values of the statements

~p : It is not a Labor day - Truth value (F)

~q : I will not go to the park - Truth value (F)

Now (~q ∧ r) : I will not go to the park and have a picnic with my family - Truth value (F) [ conjunction of two statements having truth values as True will be true otherwise False ]

~p → (~p ∧ r) : If it is not Labor Day, then I will not go to the park and have a picnic with my family : Truth value (F) [ Implication of two statements has the truth value as False only when first statement is True and second statement is False otherwise truth value will be True ]

Option C. is the answer.