The following statement `(p to q) to [(~p to q) to q]` is

Options

A. equivalent to ` p to ~ q`
B. a fallocy
C. a tautology
D. equivalent to ` ~ p to q`

Answer

C

Explanation

We know that ` p to q = ~ p vv q `
` ~ p to q cong p vv q`
` and , (~ p to q) to q = ( p vv q) to q = ~ ( p vv q) vv q`
` ( ~ p ^^ ~q) vv q = ( ~ p vv q) ^^ ( ~ q vv q)`
` = ( ~ p vv q) ^^ t = ~ p vv q =p to q`
Hence, ` ( p to q ) to [ ( ~p to q) to q]`
` = ( p to q) to (p to q) ` , which is a tautology.