could anyone help with any part of this i think part 3 and 5 are symmetric im not sure about the rest

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- February 2nd 2009, 06:57 AManon18help on relation
could anyone help with any part of this i think part 3 and 5 are symmetric im not sure about the rest

- February 3rd 2009, 10:44 AMstapel
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Which of the following relationson sets**R**are reflexive, symmetric, transitive? Give proofs or counterexamples.**X**

- if and only if divides
- if and only if
- if and only if
- if and only if is a multiple of 5
- is the set of countries in Europe, if and only if and have a common border.

- February 3rd 2009, 11:13 AMReferosQuote:

i think part 3 and 5 are symmetric im not sure about the rest

i. Not symmetric. For instance, 1 divides 5, but 5 doesn't divide 1.

ii. Not symmetric. For instance is true, but is false.

iii. Symmetric. If , then

iv. Symmetric. If , A is an integer, then . In both cases, and are multiples of five.

v. Symmetric. If shares a border with , then shares a border with .

- February 4th 2009, 04:11 AManon18
any idea which of the others are relexive or transitive?

- February 4th 2009, 04:38 AMPlato
Well, iii is an equivalence relation so it is all three: reflexive, symmetric and transitive.

For v, does any county share a border with itself? If so then that relation is reflexive.

Do that for each of the other relations: is it true that each term is related to itself?

Is this true: means that ? If so, then the relation is transitive.