When I am solving option (b) , after simplification , I get (~a +1+ c ) . So , for a=1 , b=0 , c=0 , output is 1.

and when I solve option (d) , after simplification I get (~a+~b+c) .

So , option (b) is tautology

and when I solve option (d) , after simplification I get (~a+~b+c) .

So , option (b) is tautology