Question

I need to find the truth value of the compound statement:

p ^ (q V ~ r)

where p represents a true statement
while q and r represent false statements

true or false

Answer 1

p ^ (q V ~ r ) = (p ^ q) V (p ^ ~ r)

Answer 2

so for the statement to be true, either (p^q) or (p ^ ~ r) has to be true.

Answer 3

p^q is true iff both p and q are true, but q is not, so p ^ q is false..
p ^ ~r is true iff p is true and r is false, which is the case. so p ^ ~r is true

Answer 4

hence, the compound statement is true.