Q. Which of the following statement is a tautology
A) $( \sim q \land p) \land q$
B) $( \sim q \land p) \land (p \land \sim p)$
C) $( \sim q \land p) \vee (p \land \sim p)$
D) $(p \land q) \land ( \sim (p \land q))$
Explanation
(c)
Truth table
[table] $p$ | $q$ | $\sim p$ | $\sim q$ | $\sim q \land p$ | $( \sim q \land p) \land q$ | $(p \land \sim p)$ | $( \sim q \land p) \vee (p \land \sim p)$ | $( \sim q \land p) \vee (p \land \sim p)$ ; T
T
F
F | T
F
T
F | F
F
T
T | F
T
F
T | F
T
F
F | F
F
F
F | T
T
T
T | F
F
F
F | T
T
T
T [/table]
It is clear from the table that last column have all true values. Hence option (c) is correct
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.