Statements -1 : `~(pharr~q)` is equivalent to `p harr q`
Statement-2: `(~ p harr ~q)` is a tautology.

Options

A. Statement-1 is True, Statement -2 is Ture, Statement -2 is a correct explanation for statement -2
B. Statement-1 is True, Statement -2 is True,, Statement -2 is not a correct explanation for statement -2
C. Statement -1 is True , Statement -2 is false.
D. Statement -1 is False, statement -2 is True.

Answer

C

Explanation

Let ` r_(1)` be the statement ` ~ ( p harr ~ q) ` then .
` r_(1) = ~ ( p harr ~ q)`
` Rightarrow r_(1) -~ {~( p vv ~ q) ^^ ( p vv q) } [ therefore p harr q -( p vv ~ q) ^^ ( q vv ~ p)]`
` r_(1) =- ~ {~ ( p ^^ q) ^^ ( p vv q)}`
` Rightarrow r_(1) = ( p ^^ q) vv ( ~ p ^^ ~ q)`
` Rightarrow r_(1) = {( p ^^ q) vv ~ p } { p ^^ q) vv ~ q}`
`Rightarrow r_(1)=(t^^( q vv~p)}^^ {(q vvq)^^t}`
` Rightarrow r_(1) = ( q vv ~ p) ^^ ( p vv ~ q)`
` Rightarrow r_(1) ( p harr q)`
So , statement -1 is true .