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

In summary, in the conversation, the question is asked about whether a relation in a set of people, "is brother of", is symmetric. The answer is no, as it depends on gender rather than age. The explanation is given with an example and further clarifications are provided. Another question is asked about finding the domain and range of a given equation, and the correct answer is given with an explanation. The conversation ends with a thank you.
  • #1
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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?
 
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  • #2
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.
 
  • #3
Ohhhhh right why couldn't i think about that. Anne is name of girl indeed..
Thankyou!
 
  • #4
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
 
  • #5
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: [itex]y=\frac{1}{2} \Rightarrow x=\frac{1}{2}\sqrt{35} \notin \mathbb{Z}[/itex]
 
  • #6
Right..ahh why couldn't i think about such things before register the replies..
Thankyou!
 

1. What is a symmetric relation?

A symmetric relation is a type of mathematical relation where the order of the elements does not matter. In other words, if a relation R contains the elements (a, b), then it also contains the elements (b, a).

2. How is symmetry determined in a relation?

In order to determine if a relation is symmetric, you can check if every pair of elements in the relation has a corresponding pair with the elements in the opposite order. If this is true, then the relation is symmetric.

3. Is "is brother of" a symmetric relation?

Yes, "is brother of" is a symmetric relation. If person A is the brother of person B, then person B is also the brother of person A.

4. Can a relation be both symmetric and asymmetric?

No, a relation cannot be both symmetric and asymmetric. These are two opposite properties of relations. A relation is either symmetric, meaning it follows the rule stated in question 2, or it is asymmetric, meaning it does not follow this rule.

5. Are there any real-life examples of symmetric relations?

Yes, there are many real-life examples of symmetric relations. One example is the "is married to" relation. If person A is married to person B, then person B is also married to person A. Another example is the "is friends with" relation. If person A is friends with person B, then person B is also friends with person A.

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