"Symmetric Relations: Is "Is Brother of" Symmetric?

[385sk117]

Homework Statement

Is this relation symmetric?

The relation in a set of people, "is brother of"

Homework Equations

aRb , bRa

The Attempt at a Solution

The answer is not symmetric. They gave example says that
paul may be the bother of Anne but Anne is not the brother of paul
I thought that if A is brother of B then automatically B is brother of A isn't it?
I think the reason why i can not understand this is problem of English.
In my country brother indicates both older and younger, is it different in other country?

 

[Cyosis]

It does seem like a linguistic problem. Paul is male Anne is female. Paul is the brother of Anne, Anne is the sister of Paul. It has nothing to do with age only with gender. I hope this clears things up.

A few more clarifications. If the set would have been the set of all males then the relation would have been symmetric.

 

[385sk117]

Ohhhhh right why couldn't i think about that. Anne is name of girl indeed..
Thankyou!

 

[385sk117]

an one more question
{(x,y) l x^2 + y^2 = 9, x belongs to Z}
I have to find the domain and range here and as x belongs to Z [interger]
I thought the domain is all the integers. and if x = 5 then y^2 = -16 which gives answer
y = 4i so range is all the complex numbers. But the answer is
domain {-3,-2,-1,0,1,2,3}
range {-3, -2(root2), -(root5), 0 , root5,2 root 2, 3

 

[Cyosis]

It is the equation of a circle with radius 3. You can be pretty sure that they want real values for y and not complex values. Secondly even if we were to allow complex values for y then the range would still not be all the complex numbers. Example: y=\frac{1}{2} \Rightarrow x=\frac{1}{2}\sqrt{35} \notin \mathbb{Z}

 

[385sk117]

Right..ahh why couldn't i think about such things before register the replies..
Thankyou!