SOLUTION: Determine whether the relation on the set of all real numbers is reflexive, symmetric ,antisymmetric , and transitive when (x ,y) �R if and only if 1) x + y= 0 2) x = +,- y 3)x

SOLUTION: Determine whether the relation on the set of all real numbers is reflexive, symmetric ,antisymmetric , and transitive when (x ,y) �R if and only if 1) x + y= 0 2) x = +,- y 3)x

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Question 993909: Determine whether the relation on the set of all real numbers is reflexive, symmetric ,antisymmetric , and transitive when (x ,y) �R if and only if
1) x + y= 0
2) x = +,- y
3)x -y is a rational number
4)x =2y
5)xy is greater than equal to 0
6)xy= 0
7)x =1
8)x =1 or y =1
Please explain the answer
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Which is the same thing as

So if

then

, and therefore

unless

.

Therefore

is neither reflexive or irreflexive.

But since

can be negative,

Therefore, R is symmetric.

Since

except when

,

is not asymmetric.

Since if

then

, so if

then

.

Therefore R is transitive.

John

My calculator said it, I believe it, that settles it

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