I have been asked to determine whether this binary relation is reflexive or irreflexive and symmetric

Question

I have been asked to determine whether this binary relation is reflexive or irreflexive and symmetric or not

On the set $\{1,2,3\}$, the relation
$\{(1,1), (1,2), (2,2), (3,3) \}$

I haven't been given any more information.

Would I be correct in saying that it is reflexive due to $(1,1), (2,2), (3,3)$ all belonging to the set given?

Also, I have stated it is not symmetric due to some of the relation not belonging to the set?

I apologise if I don't make much sense there, I'm new to this and trying to learn if someone could explain if I'm on the right lines or completely off?

Thank you for your time.

Answer 1

Q1: Indeed, you're correct. Since for all $a$ elements in your set $S$, $(a, a) \in $ your relation $R$.

Q2: If you're trying to ask if you can state that it's not symmetric due to some pair not being in $R$, then indeed you can, as long as you prove why. In this particular case, $R$ is clearly not symmetric because $(1,2) \in R$ but $(2,1) \notin R$. What about antisymmetry, however?

Answer 2

A relation R on a set X(ie,R is a subset of X cross X) is said to be reflexive if xRx for all x belongs to X. Here,X={1,2,3},also given that,{(1,2),(2,2,),(3,3)} belongs to R, which means it is reflexive. A relation is said to be symmetric if xRy implies yRx,where x,y belongs to X. In the question it is given that,(1,2) belongs to R but (2,1) not belongs to R.Hence it is not symmetric.