# Question about Properties of Relations

• Learning_Math
In summary, the conversation discussed the concept of reflexivity in relation to the set of all people, where xPy means x is a parent of y. The question was whether x can be the parent of x, and it was concluded that this is not possible and therefore the relation P is not reflexive. The speaker also expressed confusion about how to deal with reflexivity in this question, but was reassured by the other person's explanation.
Learning_Math
1. The question is: P on the set, A, of all people, where xPy means x is a parent of y.

## Homework Equations

- None

3. Attempts at a Solution Here is where I am confused. Reflexivity is defined by aRa. So I am unclear what to do with more than one variable. So in this question, do I examine if xRx? That is to say is x a parent of x? If that is the case, then the answer is clearly no. I am just unsure of how to deal with reflexivity.

I am ok with symmetry and transitivity.

Can x be the parent of x? IOW, can someone be his or her own parent?

Okay, so am I correct in what to do with reflexivity in this question? It is obviously absurd that x can be the parent of x. Where I am unclear is if that is the question I need to be asking vis-a-vis reflexivity.

I thought I was pretty clear - the relation P is not reflexive.

Mark44 said:
I thought I was pretty clear - the relation P is not reflexive.

You were pretty clear. I am just at the very end of my proof writing class, and it has me pretty jumpy. Thanks for your help.

## What are properties of relations?

Properties of relations are characteristics or attributes that describe the relationship between two or more objects or elements. They can include properties such as reflexivity, symmetry, transitivity, and antisymmetry.

## What is reflexivity in relation properties?

Reflexivity in relation properties refers to the property that every element in a relation is related to itself. In other words, for every element A in a relation R, (A, A) is an ordered pair in R.

## What is symmetry in relation properties?

Symmetry in relation properties refers to the property that if (A, B) is an ordered pair in a relation R, then (B, A) is also an ordered pair in R. This means that the direction of the relationship between two elements does not matter.

## What is transitivity in relation properties?

Transitivity in relation properties refers to the property that if (A, B) and (B, C) are ordered pairs in a relation R, then (A, C) is also an ordered pair in R. This means that if there is a relationship between A and B, and a relationship between B and C, then there is also a relationship between A and C.

## What is antisymmetry in relation properties?

Antisymmetry in relation properties refers to the property that if (A, B) and (B, A) are ordered pairs in a relation R, then A = B. This means that there cannot be both a relationship and a reverse relationship between two elements in a relation.

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