Which of the following statement is a tautology?

Options

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

Answer

A

Explanation

Using truth table
`{:(p,q,r,p^^q,~(p^^q),pvvr,vv~(p^^q)),(T,T,T,T,F,T,T),(T,T,F,T,F,T,T),(T,F,T,F,T,T,T),(T,F,F,F,T,T,T),(F,T,T,F,T,T,T),(F,T,F,F,T,F,T),(F,F,T,F,T,T,T),(F,F,F,F,T,F,T):}`
`{:(P,~P,Q,~p^^q,~pvvq,(~p^^q)vv(~pvvq)),(F,T,T,T,T,T),(F,T,F,F,T,T),(T,F,T,F,T,T),(T,F,F,F,F,F):}`
`{:(pvvq,~q,((pvvq)^^~q),~((pvvq)^^~q)),(T,F,F,T),(F,T,F,T),(F,F,F,T),(T,T,T,F):}`
`{:(prarrq,qrarr r,(prarrq)^^(q^^r)),(T,T,T),(T,F,F),(F,T,F),(F,F,F):}`