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

Algebra ->  College  -> Linear Algebra -> 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       Log On


   

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) About Me  (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