Choose the correct alternatives (more than one may be correct) and write the corresponding letters only:
Which of the following is/are a tautology?
$\left(a \wedge b \right) \to b \vee c$
$\implies \neg \left(a \wedge b \right) \vee b \vee c$
$\implies \neg a \vee \neg b \vee b \vee c$
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
Option b is tautology.