Truth table for implies

We would normally use (A implies B) as a conditional statement and not so much as a statement that is true or false. But apparently in many cases it is considered as a logical statement which can either be true or false. The truth table for (A implies B) or (A=>B) is given as follows:

A B A implies B
T T T
T F F
F T T
F F T

 

It’s quite difficult to wrap your head around this. I’ve tried a lot and have now accepted it for what it is. I’m sure I’ll get round to it sometime in the future and when I have more clarity about it, I’ll post here. For now, understand that it’s identical to evaluating ((Not A) or B)

A B Not A (Not A) OR B
T T F T
T F F F
F T T T
F F T T
One way to remember is like this –
  • If A is False, then it doesn’t matter what B is, A=>B  will always be True
  • If A is True, then A=>B will be True only if B is also True.
    Think about this and leave a comment if you have anything to add.
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