# 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 : $\dpi{100} \sim (p\leftrightarrow \sim q)\;$ is equivalent to $\dpi{100} p\leftrightarrow q$Statement- 2 : $\dpi{100} \sim (p\leftrightarrow \sim q)\;$   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

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.

-

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

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$\sim \left ( p\leftrightarrow \sim q \right )$ 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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