Directions : Questions are Assertion- Reason type questions. Each of these questions contains two statements :

Statement- 1 (Assertion) and Statement - 2 (Reason).

Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.

Question :

Statement- 1 : \sim (p\leftrightarrow \sim q)\; is equivalent to p\leftrightarrow q

Statement- 2 : \sim (p\leftrightarrow \sim q)\;   is a tautology.

  • Option 1)

    Statement-1 is true,Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

  • Option 2)

    Statement- 1 is true, Statement-2 is false

  • Option 3)

    Statement-1 is false, Statement-2 is true

  • Option 4)

    Statement-1 is true, Statement-2 is true; Statement-2 is correct explanation for Statement-1

 

Answers (1)

As we learnt in

If and only if -

p\Leftrightarrow q:(p\Rightarrow q)\wedge (q\Rightarrow p)

-

 

 

Tautology -

A statement pattern is called tautalogy, if it is always true, whatever may be the truth values of constitute statements.

-

 

 

Fallacy or contradiction -

A statement pattern is called a fallacy if it is always false, whatever may be the truth values of its constituent statements.

-

 

 \sim \left ( p\leftrightarrow \sim q \right ) is equivalent  to   p\leftrightarrow q

as their truth tables are identical.

But truth table of  \sim \left ( p\leftrightarrow \sim q \right ) has false results as well, so it is not a tautology.


Option 1)

Statement-1 is true,Statement-2 is true; Statement-2 is not a correct explanation for Statement-1

Incorrect option

Option 2)

Statement- 1 is true, Statement-2 is false

Correct option

Option 3)

Statement-1 is false, Statement-2 is true

Incorrect option

Option 4)

Statement-1 is true, Statement-2 is true; Statement-2 is correct explanation for Statement-1

Incorrect option

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