I was just learning the truth table of the propositional logic . I understand the truth table for the conjunction and disjunction because they make sense in the real life. The conjunction A∧B means "A and B", and it is intuitively correct that "A and B" is true iff both A is true and B is true. The disjunction A∨B means "A or B", and it makes sense also that unless both A and B are false, A∨B is true. But for the material implication, A implies B, I can't really get the truth table. For example:
Let A be the statement that "I washed my dishes today." Let B be the statement that "It rained yesterday."
Assumed that both statements are true, then according to the material implication, A implies B is also true, but there is no single connection between the chores and the weather. It sounds a little bit bizarre to say that "because I washed my dishes today, so it rained yesterday". That just sounds weird.
So why does the truth table of material implication be like that?