/sci/ - Science & Math

Hi can someone help me understand something?
I'm trying to teach myself math and am reading Logic: the Laws of Truth and am stumped at one part about implications.

It says if someone says something that is translated into PL as A, then that implies A ∨ B. and that
A
∴
A ∨ B
is a valid argument.
But this doesn't make sense to me because if the argument A is false then there can still be a conclusion that's true if B is true.
So what am I missing??