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Mathematical Reasoning
hard
The statement $p \to ( q \to p)$ is equivalent to
A
$p \to q$
B
$p\, \to \,(p \vee q)$
C
$p\, \to \,(p \to q)$
D
$p\, \to \,(p \wedge q)$
(JEE MAIN-2013)
Solution
| $q$ | $p$ | ${q \to p}$ | $p \to \left( {q \to p} \right)$ | ${p \vee q}$ | $p \to \left( {p \vee q} \right)$ |
| $T$ | $T$ | $T$ | $T$ | $T$ | $T$ |
| $T$ | $F$ | $F$ | $T$ | $T$ | $T$ |
| $F$ | $T$ | $T$ | $T$ | $T$ | $T$ |
| $F$ | $F$ | $T$ | $T$ | $F$ | $T$ |
Since truth value of $p \to \left( {q \to p} \right)$ and $p \to \left( {p \vee q} \right)$ are same, hence $p \to \left( {q \to p} \right)$ is equivalent to $p \to \left( {p \vee q} \right)$.
Standard 11
Mathematics
