Implication
There’s the bog standard Logical Connectives you’re already used to; and, or, not etc. There is a new one to consider: Implies. The symbol is A → B , read as “A implies B”
Consider the statement: “If you study hard, then you will pass the test”. Studying hard will be A and passing the test will be B. The truth table for the statement as a whole is to the right.
If A is false, then we can’t really deduce anything about the actual statement. The statement tells us nothing about what actually happens if we don’t study. Thus, the statement could still hold True. Therefore, if A is ever False, the implicative is True.
