# The statement $\dpi{100} p\rightarrow (q\rightarrow p)$ is equivalent to Option 1) $p\rightarrow (p\leftrightarrow q)\;$ Option 2) $\; p\rightarrow (p\rightarrow q)\;$ Option 3) $\; p\rightarrow (p\vee q)\;$ Option 4) $\; p\rightarrow (p\wedge q)$

As we learnt in

Truth Table of "if-then" -

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Truth table of 'OR' operator -

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$p\rightarrow \left ( q\rightarrow p \right )$

 $p$ $q$ $q\rightarrow p$ $p\rightarrow \left ( q\rightarrow p \right )$ $p\rightarrow \left \left ( p\vee q \right )$ T T T T T T F T T T F T F T T F F T T T

Both are tautologies.

Option 1)

$p\rightarrow (p\leftrightarrow q)\;$

Incorrect option

Option 2)

$\; p\rightarrow (p\rightarrow q)\;$

Incorrect option

Option 3)

$\; p\rightarrow (p\vee q)\;$

Correct option

Option 4)

$\; p\rightarrow (p\wedge q)$

Incorrect option

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