Q. If $(p \land \sim r) \rightarrow (\sim p \vee q)$ is false, then the truth values of $p,\ q\ and\ r$are respectively
A) T, F and F
B) F, F and T
C) F, T and T
D) T, F and T
Explanation
(a)
Truth Table
[table] $p$ | $q$ | $r$ | $\sim p$ | $\sim r$ | $p \land \sim r$ | $( \sim p$
$\vee q)$ | $(p \land \sim r) \rightarrow$
$(\sim p \vee q)$ ; T
T
T
T
F
F
F
F | T
T
F
F
T
T
F
F | T
F
T
F
T
F
T
F | F
F
F
F
T
T
T
T | F
T
F
T
F
T
F
T | F
T
F
T
F
F
F
F | T
T
F
F
T
T
T
T | T
T
T
F
T
T
T
T [/table]
Hence, $(p \land \sim r) \rightarrow (\sim p \vee q)$ is F.
When $p = T,\ q = F,\ r = F$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.