Boolean Implication

Question

I need some help with this Boolean Implication.

Can someone explain how this works in simple terms:

A implies B = B + A' (if A then B). Also equivalent to A >= B

Answer 1

Boolean implication A implies B simply means "if A is true, then B must be true". This implies (pun intended) that if A isn't true, then B can be anything. Thus:

False implies False -> True
False implies True  -> True
True  implies False -> False
True  implies True  -> True

This can also be read as (not A) or B - i.e. "either A is false, or B must be true".

Answer 2

Here's how I think about it:

if(A)
  return B;
else
  return True;

if A is true, then b is relevant and should be checked, otherwise, ignore B and return true.