Q. Which of the following statements is a tautology?
A) $(\sim q \land p) \land q$
B) $(\sim q \land p) \land (p \land \sim p)$
C) $(\sim q \land p) \vee (p \vee \sim p)$
D) $(p \land q) \land (\sim(p \land q))$
Explanation
(c)
Truth Table
[table] $p$ | $q$ | $\sim p$ | $\sim q$ | $\sim q \land p$ | $( \sim q \land p)$
$\land q$ | $p \vee \sim p$ | $(p \land q) \land$
$( \sim (p \land q))$ | $( \sim q \land p)$
$\vee$
$(p \vee \sim p)$ ; 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 the last column has all true values.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.