Thread: Translate the logical expression into good English

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 denition 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?

Regards

Originally Posted by Snowboarder

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.

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.

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.

Originally Posted by Snowboarder

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.

What do you think? It asks for a translation.

i presume that is the same but presume is not enough for me . It is quite confusing topic or maybe I'm just dumb.

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?

You wouldn't be doing compsci 225 at auckland uni would you snowboarder? ;D

yes i'm doing . just wanna get ride off it and start doing another assignment. on this forum is a lot of smart people that can help you figure out some silly problems