Implication - interesting word ?
A while ago, I and a few friends discussed the logic behind implications. Since it was a bit confusing to us in the beginning, I’ll use this to try and explain.
Implications come in the form “x implies y”, “if x then y”, and “y if x.” Essentially, these statements mean “if x is true, then y must be true.” Here are some examples:
If you go to Cambridge, then you hate Oxford.
I will lose weight if I don’t eat dessert.
x=3 implies x+2=5.
A helpful way to view an implication is as a promise. For example, Statement 1 can be rewritten as “You are guaranteed to hate Oxford provided you go to Cambridge.”
Now, lets break it down.
Case 1. Lets say you do go to Cambridge (lucky you!). If you hate Oxford, then the promise holds and Statement 1 is true. If you don’t hate Oxford, then the promise is broken and Statement 1 is false.
Case 2. Now, you don’t go to Cambridge. Since you don’t go to Cambridge, you are not guaranteed to hate Oxford. But, you are also not guaranteed to love (not-hate) Oxford. So, regardless of whether you love or hate Oxford, the statement “If you go to Cambridge, then you hate Oxford” is true.
Remember that a false statement implies anything.
I think I got that right ? I don't mean to imply anything by the way.