Which of the following statements is contingency?

Options

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

Answer

C

Explanation

Option (1) `(p vv q) vv ~q`
`-=p vv (q vv ~q)-=p vvT`
`-=T` which is tautology.
option (3) `(p vvq) ^^ ~q`
`-=(p ^^ ~ q) vv (q ^^ ~ q) -= (p ^^ ~q) vvF`
`-=(p ^^ ~ q)`
if `p to T, q to T`
Then `p ^^ ~q to F`
if `p to T, q to F`
then `p ^^ ~ q to F`
then `p ^^ ~q to T`
So, `(p ^^ ~ q)` is a contigency.
therefore statement `(p vv q) ^^ ~ q` is contingency.