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Sets, Relations and Function - JEE Mathematics question (JEE Main 2017 (Offline))

JEE Main 2017 (Offline)Question 1
The statement $(p\to q)\to\left((\sim p\to q)\to q\right)$ is :
Sets, Relations and Function
Options for question 1, choose one

Solution

$(\sim p\to q)\equiv p\vee q$, and $(p\to q)\wedge(p\vee q)\Rightarrow q$ in both cases $p=T$ and $p=F$, so $(p\to q)\to((\sim p\to q)\to q)$ is always true: a tautology.

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