Hi all. Does anybody would help me with my question with predicates?
Let p(x, y) denote the predicate "x <= y" and let q(x, y) with domain of denition N x N.
For all x For all y For all z ((p(x,y) ^ p(y,z) -> p(x,z))
I need to translate this into good english and say if it's right or false. So thats what i did:
For all x, y and z natural numbers if number y is bigger or equal to x and if number z is bigger than y than z is bigger than x.
Please somebody help me I'm getting confused with this z and how can i state whether the proposition is true?
Is "If a is natural number that is at least as large as the natural number b and b is at least as large as the natural number c then a at least a large as c." the same as"
If x is natural number that is at least as large as the natural number y and y is at least as large as the natural number z then x is at least large as z.
BTW thank you for fast respond.
Thank you plato for your respond. What about this example:
For all x For all y [There exist an z(Q(x,z) ^ Q(z,y)) -> Q(x,y)]
It exist natural number z that is bigger than all natural numbers x and it exist natural number z that is smaller than all natural numbers y then all natural numbers x are smaller than all natural numbers y.
And that would be false right?