Assume p is true q is true and r is false What is the truth

Assume p is true, q is true, and r is false. What is the truth value for the compound statement:

( p ^ q ) ^ r

a. True

b. False

Solution

p is TRUE

q is TRUE

r is FALSE

Consider the following TRUTH TABLE for AND Operation between A and B

i)

The statment p^q implies (p AND q) which is (TRUE AND TRUE) which is TRUE

ii)

The statement (p^q)^r implies ((p AND q) AND r). From above, the statement can be rewritten as ((TRUE AND FALSE).

From Truth Table above, (TRUE AND FALSE)=FALSE. Therefore,

(p^q)^r=FALSE

Hence, answer is Option b: FALSE