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

Options

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

Answer

B

Explanation

`(p to q) to {(~p to q) to q}`
`=(p to q) to {(p vvq) to q}`
`=( p to q) to {(~p to ~q) vvq}`
`=(p to q) to {(~p vvq) ^^(~qvvq)}`
`=(p to q) to (~p vvq)`
`=( pto q) to (p to q) `
=T