Question:-
Which of the following are tautology?
(i)[p ^ (p->q)]->q
(ii)
(iii)
Option (A)
Only (i) and (ii)
Option (B)
Only (ii) and (iii)
Option(C)
Only (i) and (iii)
Option(D)
All (i), (ii) and (iii)
Correct Option:
(D)
Question Solution:
Put ^ -> . and ∨ -> +
(i)[p ^ (p->q)]->q
=
= pq->q =
=
=
So (i) is tautology.
(ii) (ii) is tautology in the same way as (i)
(iii)
=
=
=
=
=
So (iii) is also topology.
Hence option (d) is true.
Note:
This problem can be done more easily if the following is observed.
(i) is modus ponens and hence is tautology.
(ii) since p -> q , therefore is a tautology.
(iii) is modus tollens and hence is tautology.
question-answer-faq-14673