1.

Which of the following statements is contingency?

Answer»

<P>`(pvvq)vv ~Q`
`(p vv q) V~q`
`(p vvq) ^^ ~q`
`p to ( p vv q)`

Solution :OPTION (1) `(p vv q) vv ~ q`
`-= p vv (q vv q) -= p vv T`
`-= T` which is a TAUTOLOGY.
Option (2) `(p vv q) v ~`
`-= (p vv ~ p) vv q -= T vv q`
`-= T` which is tautology.
Option (3) `(p vv q) ^^ ~q`
`-= (p ^^ q) vv (q ^^ ~ q) -= ( p ^^ ~ q) vv F`
`-= (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 T`
So, `(p ^^ ~q)` is a contingency.
Therefore statement `(p vv q) ^^ ~ q` is contingency.


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