Which relations are partial orders

Question

I have come across the following question on a practice test:

Which of the following relations defined on $X = \{1, 2, 3\}$ are partial orders?

$(1) \; \{(1, 1),(2, 2),(3, 3)\}$

$(2) \; \{(1, 2),(2, 1),(2, 2),(3, 3)\}$

$(3) \; \{(1, 1),(2, 1),(2, 2),(1, 3),(3, 3),(3, 1)\}$

$(4) \; \{(1, 1),(2, 2),(1, 3),(1, 2)\}$

$(5) \; \{(1, 1),(2, 2),(3, 3),(1, 3),(1, 2)\}$

My answer would be that $1$ and $5$ are partial orders on $X$. This is due to $(2)$ and $(3)$ having the symmetric property and $(4)$ not being reflexive.

Can anyone validate my answer?

Answer 1

I agree with your solution. Good work supplying your working.

(I don't have enough reputation to comment so I'm submitting this as an answer)