Which of the following is wrong?

Options

A. ` p to q` is logically equivation to ` ~p vv q`
B. if The truth values of p,q,r are T,F,R respectively, then the truth value of ` ( p vv q) ^^ ( q ^^ r) ` is T
C. ` ~ ( p vv q vv r) cong -~ p ^^ ~ q ^^ ~ r`
D. the truth value of ` p ^^ ~ ( p vv q)` is always T

Answer

D

Explanation

The truth table of ` p to q and ~ p vv q` are given below.

Clearly, truth tables of `p to q and ~ p vv q` are same.
So, ` p to q` is logically equivalent to ` ~ p vv q`
Hence, option (a) is correct
If the truth values of p,q,r are T,F,T respectively, then the truth values of ` p vv q and q vv r` are each equal to T. therefore, the truth value of `( p vv q) ^^ (q vv r)` is T.
Hence, option (b) is correct.
We, have.
` ~ ( p vv q vv r) cong ( ~ p vv ~ q ^^ ~ r)`
So, option , (c) is correct.
If p is true and q is false, then ` p vv q` is true. consequently,
` ~ ( p vv q) ` is false and hence ` p ^^ ~ ( p vv q)` is false.
Hence, option (d) is wrong.