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# Implications

The first logical operator we will cover is the implication operator. The notation we will be using for implication or implies operator is the arrow(->). Some of the other common symbols that are used for implies are: So now that you know what it looks like what exactly does implication mean? Implication is one of the most used signs and is present in any logical statement where you are saying If A Then B. We can write this as A -> B or A IMPLIES B.

So if we think about it we can conclude that if A is true then B is also true. It just makes sense or of course it is logical. We would also conclude that if A was true and B was false then this statement wouldn't make sense and so would be false. So the truth table for this would be:

ABA->B
TT T
TFF

Now you might also want to say that if A is False then B is False but this is not the case. When A is False we cannot conclude that B is true or that it is False. Both are a true statement. So adding these to the table we get:

ABA->B
TT T
TFF
FTT
FFT

This may seem weird but a simple way to remember it is that if the first proposition is false then it doesnât matter what the second proposition is, the implication of the statement will always be true. If you think of examples they do make sense take the example of "If it's raining I wear my raincoat". Maybe it's not raining but i'm wearing my raincoat cause I think it will rain. Anyways just remember the fact that if A is False it doesn't matter what B is.