Made Easy Test Series

Question

p ->(q->r).

 

Could you please tell me how it is a tautology?

Comments

The answer I’m getting is 1,1,1,1,1,1,0,1.  So, its contingency.

please let me know if I'm wrong

Answer 1

Solving it by Case method,

Case 1 : P is True

p → (q → r) = T → (q → r) = q→ r [We could stop here itself as it’s contingency, depending on values of q and r]

Case 2 : P is False

p → (q → r) = F → (q → r) = T

 

Hence, its not a tautology but a contingency.

Comments

@chokostar Nice. 

Another Method (Digital Logic method):-

Since it is not 1, hence it is not Tautology.