Hello. I need help on determining this relation.

Determine the relation defined with for numbers

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- Jan 21st 2009, 07:53 PMjavaxRelation
Hello. I need help on determining this relation.

Determine the relation defined with for numbers - Jan 21st 2009, 08:06 PMJhevon
- Jan 21st 2009, 08:11 PMjavax
- Jan 21st 2009, 08:42 PMJhevon
- Jan 22nd 2009, 08:29 AMjavax
- Jan 22nd 2009, 11:14 AMJhevon
- Jan 22nd 2009, 01:47 PMjavax
- Jan 22nd 2009, 01:51 PMJhevon
actually, 1, 3 & 4 makes a partial order relation.

ok, so check if it is an equivalence relation:

(1) does x relate to itself? can you find and integer such that x = zx?

(2) do we have symmetry. if we can find and integer z so that y = zx, will we always be able to find an integer n so that x = ny?

(3) do we have transitivity? if we have integers n and m so that a = mb and b = nc, can we find an integer k so that a = kc? - Jan 22nd 2009, 02:44 PMjavax
- Jan 22nd 2009, 02:53 PMJhevon
brilliant!

Quote:

(2) (s) ,

if we multiply these we have For we have (Does this mean that we have a symmetry?

take y = 2 and x = 1. clearly y relates to x, since y = zx (where z = 2).

but does x relate to y? can we find an integer k so that x = ky, that is, 1 = k*2?

Quote:

(3) (t) . I multiplied again

sub.

What do you think?

- Jan 22nd 2009, 03:07 PMjavax
- Jan 22nd 2009, 03:10 PMJhevon
- Jan 22nd 2009, 03:12 PMjavax
- Jan 22nd 2009, 03:18 PMJhevon
no, anti-symmetric is defined by the fourth definition you have. after reading a few math books you should start to see how mathematicians define things. if anti-symmetric means "not symmetric" that is exactly how they would define it. it shouldn't be hard to come up with an example of a relation that is both not symmetric and not anti-symmetric. see here

you have to check if it is anti-symmetric. if it is, we have an order relation (since you already showed we have reflexivity and transitivity)