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

Option C. is the answer.

Step-by-step 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.

1) c 2143.6 cm

2) c 113.0 m

3) a 33.5 ft

4)   d 2 cm

5) c 20 mm

6) 180 in

7) d 120 ft