1 Determine whether pVq p r q r r is a tautology And e

1. Determine whether [(pVq) ^ (p -> r ) ^ (q -> r)] -> r is a tautology. And explain why.

Solution

[(pVq) ^ (p -> r ) ^ (q -> r)] -> r

Or (( pVq) ^ (p -> r ) ^ (q -> r)) v r  

Or, ((pvq) ^ (pvr) (qvr))v r

Or, ((pvq)((pq) r)) r

Or, ((pq)((pq)r)) r

Or, ((pq) ((pq)r)) r

Or, ((p q) ((p q) r) ) r

Or,( (p q) ((p q) r)) r

Or, (((pq) ( p q)) (( p q) r)) r

Or, T ((p q) r )) r

(p v q) V T