Choose the correct alternatives (more than one may be correct) and write the corresponding letters only: Which of the following is/are a tautology?
Answer: (B) $\left(a \wedge b \right) \to b \vee c$ $\implies \neg \left(a \wedge b \right) \vee b \vee c$ $\implies \neg a \vee \neg b \vee b \vee c$ $\implies T$ Option (A) is not TRUE when C is FALSE Option (C) is not TRUE when b is TRUE and C is FALSE Option (D) is not TRUE when a and b are TRUE and C is FALSE.
How to treat option D? (the associtivity) a->(b->(b->c)) or (a->b)->(b->c)
-> is right associative according to 2nd ans by http://math.stackexchange.com/questions/12223/associativity-of-logical-connectives
Associativity like
Not>AND>OR>IMPLICATION
Option b is tautology.
@abhishekmehta4u
Nice approach