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Mathematical Reasoning
hard
The following statement $\left( {p \to q} \right) \to $ $[(\sim p\rightarrow q) \rightarrow q ]$ is
A
a fallacy
B
a tautology
C
equivalent to $\sim p \to q$
D
equivalent to $p \to \sim q$
(JEE MAIN-2017)
Solution
| $p$ | $q$ | $ \sim p$ | $p \to q$ | $ \sim p \to q$ | $\left( { \sim p \to q} \right) \to q$ | $\left( {p \to q} \right) \to \left( {\left( { \sim p \to q} \right) \to q} \right)$ |
| $T$ | $F$ | $F$ | $F$ | $T$ | $F$ | $T$ |
| $T$ | $T$ | $F$ | $T$ | $T$ | $T$ | $T$ |
| $F$ | $F$ | $T$ | $T$ | $F$ | $T$ | $T$ |
| $F$ | $F$ | $T$ | $T$ | $T$ | $T$ | $T$ |
Standard 11
Mathematics
