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

Because a logical statement in the form of “If A then B” does not provide a way for the statement to be disproven if A is false. Let’s look at your example. There are 4 possible scenarios here:

1. Bob drinks and everyone else drinks.
2. Bob drinks and everyone else doesn’t drink.
3. Bob doesn’t drink and everyone else drinks.
4. Bob doesn’t drink and everyone else doesn’t drink.

Of those 4 scenarios, only #2 breaks the original statement, making it false. If Bob doesn’t drink, then no matter what everyone else does, it doesn’t disprove the original statement. Since the statement isn’t proven false, according to the rules of logic, it must be true.