gate 1990 maths propositional logic

Question

hi sir,

In above question I made truth table and checked for equivalence but I am not able to get  tautology in any of the options.

Plz help.

regards

Piyush

Answer 1

ANS: a

P->Q=~PvQ....(1)

Q->R=~QvR....(2)

P->R=~PvR....(3)

add 1,2 then we get (Pv~R) [De-morgan's low]

then add with (3) so and get 1 as answer.other options cannot satisfy so option a is the answer