Which of the following is true for the propositions p and q ?

Options

A. p ^ q is true when at least one of p and q is true
B. ` p to q ` is true when p is true and q is false
C. `p harr q ` is true only when both p and q are ture
D. ` ~ ( p vv q)` is true only when both p and q are false

Answer

D

Explanation

we know, that ` p ^^q` is true when both p and q are true.
So, option (a) is not ture.
From the truth table of ` p to q` , we observe that `p to q` is false when p is true and q is not true.
so , option (b) is not true.
We knowm, that `p harr q` is true when either both p and q true or both are false.
so , option (c) is not true.
If p and q both are false, then
` p vv q " is false " Rightarrow ~ ( p v q)` is true.
Hence, option (d) is true.