Which of the following statement patternn is a tautology?

Options

A. `(p to q) vv q`
B. `p to (q vv p)`
C. `(p vv q) to q`
D. `p vv (q to p)`

Answer

B

Explanation

Option (a), `(p to q) vv q` ,brgt `-=(~q vv q) vv q (-= (~ p vv q)`
it is not a tautology since if p is true and q is false them `(~p vv q)` is false.
Option (b), `p to (q vv p)`
`-=~p v (q vv p)`
`-=(~q vv p) q`
`-=T vv q (because~p vv p -=T)`
it is a tautology since if q is true or false then `T vv q` must be true. Similarly, check other options.