x<3, y>1 --> (implication) x-y<2

I know that this statement is true but I am having trouble approaching the proof. New to this statement stuff as I just recently started uni but I want to get implication proofs down pack ASAP. Thx in advance.

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- Mar 14th 2008, 10:24 PMah-beeProving Statement True
x<3, y>1 --> (implication) x-y<2

I know that this statement is true but I am having trouble approaching the proof. New to this statement stuff as I just recently started uni but I want to get implication proofs down pack ASAP. Thx in advance. - Mar 14th 2008, 11:43 PMMoo
Hello,

Well, just say that as y>1, -y<-1

Hence (x<3 && -y<-1) => x-y < 3-1=2 - Mar 15th 2008, 12:24 AMah-bee
but then arent u assuming that x>a, y>b is equivalent to x-y>a-b which is a false assumption

- Mar 15th 2008, 12:38 AMMoo
Nope, i'm assuming that t<a and u<b => t+u<a+b, which is true.

It's -y<-1, but it's exactly the same as the t<b above, with t=-y and b=-1

If you prefer, it's (x<3 && -y<-1) => x+(-y) < 3+(-1)=2