Let $a$ be neither tautology nor contradiction, $b$ is tautology and $c$ is contradiction . What is the value of $a\to (b\to c)$?
It's a multiple choice question where there're following options:
the expression is a contradiction
the expression is equivalent to the negation of $a$
The second answer is correct but I don't understand why. $b\to c$ is always false. Therefore $a\to (b\to c)$ is always false. So why isn't it a contradiction?
I derived my conclusion by using the truth table in this Wikipedia article.