Q. Which of the following statement pattern is a tautology ?
Solution:
(A) $p \vee(q \rightarrow p) \equiv p \vee(\sim q \vee p) \equiv p \vee p \vee \sim q$
$\equiv p v \sim q$
(B) $\sim q \rightarrow \sim p \equiv q v \sim p$
(D) $p \wedge \sim p \equiv F$
So left is (C)
$P$
$Q$
$q \rightarrow p$
$\sim p$
$\sim p \leftrightarrow q$
$( q \rightarrow p ) \vee(\sim p \leftrightarrow q )$
T
T
T
F
F
T
T
F
T
F
T
T
F
T
F
T
T
T
F
F
T
T
F
T
| $P$ | $Q$ | $q \rightarrow p$ | $\sim p$ | $\sim p \leftrightarrow q$ | $( q \rightarrow p ) \vee(\sim p \leftrightarrow q )$ |
|---|---|---|---|---|---|
| T | T | T | F | F | T |
| T | F | T | F | T | T |
| F | T | F | T | T | T |
| F | F | T | T | F | T |