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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?

Community
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Huss
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    Your argument for $(2)$ and $(3)$ doesn't work, because a relation can be both symmetric and antisymmetric at the same time. – mrp Jun 21 '15 at 07:46
  • @mrp Thanks, after more consideration: what if I say that they are not partial orders because $(2)$ isn't reflexive and $(3)$ is not antisymmetric. – Huss Jun 21 '15 at 08:26
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    Yes, that would work. – mrp Jun 21 '15 at 09:17

1 Answers1

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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)

Ainsley Pullen
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