Q.
For the statements p and q, consider the following compound statements :
(a) $(\sim q \wedge( p \rightarrow q )) \rightarrow \sim p$
(b) $((p \vee q) \wedge \sim p) \rightarrow q$
Then which of the following statements is correct?
Solution:
(A)
p
q
$\sim q$
$p \rightarrow q$
$\sim p$
$(\sim q \wedge( p \rightarrow q ))$
T
T
F
T
F
F
T
T
F
T
F
F
F
T
F
T
F
T
T
F
T
F
F
T
T
T
T
T
(B)
p
q
$p \vee q$
$\sim p$
$(p \vee q) \wedge \sim p$
T
T
T
F
F
T
T
F
T
F
F
T
F
T
T
T
T
T
F
F
F
T
F
T
Both are tautologies
| p | q | $\sim q$ | $p \rightarrow q$ | $\sim p$ | $(\sim q \wedge( p \rightarrow q ))$ | |
| T | T | F | T | F | F | T |
| T | F | T | F | F | F | T |
| F | T | F | T | T | F | T |
| F | F | T | T | T | T | T |
| p | q | $p \vee q$ | $\sim p$ | $(p \vee q) \wedge \sim p$ | |
| T | T | T | F | F | T |
| T | F | T | F | F | T |
| F | T | T | T | T | T |
| F | F | F | T | F | T |