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Help me solve this - Mathematical reasoning - JEE Main

The statement 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)

 
Answers (1)
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As we learnt in

Truth Table of "if-then" -

Figure 4

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Truth table of 'OR' operator -

-

 

 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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