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Mathematical Reasoning
medium
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?
A
$(a)$ and $(b)$ both are not tautologies.
B
$(a)$ and $(b)$ both are tautologies.
C
$(a)$ is a tautology but not $(b).$
D
$(b)$ is a tautology but not $(a).$
(JEE MAIN-2021)
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
Standard 11
Mathematics
