Why is it that in formal logic, the phrase “If Bob drinks, then everyone drinks” is true if Bob doesn’t drink ?

Question

in other words, why are statements of the form “If A then B” always true if A is false?

In: 8

Answer 1

Just adding on previous answers, a equivalente way to write “if A then B” (A -> B) using just the basic operators (not, or, and) is “not A or B” (~A v B). Since ~A will be true in case A is false, the expression will always be true.