Question

If \[p \to \left( {p \wedge \sim q} \right)\] is false. Then find the truth value of p and q respectively.
A. F, T
B. T, F
C. F, F
D. T, T

Answer 1

Hints Make a truth table to obtain the truth values of p and q respectively.
The headers of the truth table will be p, q, \[ \sim q\] , \[\left( {p \wedge \sim q} \right)\] and \[p \to \left( {p \wedge \sim q} \right)\].

Complete step by step solution
The truth table is given by,

p	q	\[ \sim q\]	\[\left( {p \wedge \sim q} \right)\]	\[p \to \left( {p \wedge \sim q} \right)\]
T	T	F	F	F
T	F	T	T	T
F	T	F	F	T
F	F	T	F	T

So, from the first row of the table we can see that \[p \to \left( {p \wedge \sim q} \right)\] is false for p and q both true.
The correct option is D.

Note Sometimes students do not have the idea how to solve this type of question, so in this type of question we need to make a truth table to get the required value.