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  • Help me solve this - Mathematical reasoning - JEE Main-3

The statement   \sim \left ( p\leftrightarrow \sim q \right )  is :

  • Option 1)

      a tautology   
     

  • Option 2)

    a fallacy  
     

  • Option 3)

    equivalent to  p\leftrightarrow q
     

  • Option 4)

     equivalent to  \sim p\leftrightarrow q

 

Answers (1)

As we learnt in

Truth Table of "if and only if" -

Figure 5

-

 

 

Truth Table of "NOT" operator -

-

 

 

p
q
\sim q
 ( p\leftrightarrow\sim q\left \right )
\sim \left ( p\leftrightarrow \sim q \right )
T T F F T
T F T T F
F T F T F
F F T F T

This is the same truth table as p\leftrightarrow q


Option 1)

  a tautology   
 

Incorrect

Option 2)

a fallacy  
 

Incorrect

Option 3)

equivalent to  p\leftrightarrow q
 

Correct

Option 4)

 equivalent to  \sim p\leftrightarrow q

Incorrect

Posted by

Vakul

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