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Q. The statement $p \rightarrow \left(q\,\rightarrow \,p\right) $ is equivalent to:

JEE MainJEE Main 2013Mathematical Reasoning

Solution:

p q $q \rightarrow p$ $p \rightarrow\left(q \rightarrow p\right)$ $p\,\vee\,q$ $p \rightarrow \left(p\,\vee \,q\right)$
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 $p \rightarrow \left(q\,\rightarrow \,p\right)$ and $p \rightarrow \left(p\,\vee\,q\right)$ are same, hence $p \rightarrow \left(q\,\rightarrow \,p\right)$ is equivalent to $p \rightarrow \left(p\,\vee \,q\right).$