R is defined on $\mathbb{N} × \mathbb{N}$ by $(a, b)R(c, d)$ iff $a \leq c$ and $b \leq d$.
I think it's reflexive and transitive. Not too sure about it being symmetric or antisymmetric.
Any help would be appreciated!
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Try a few examples. Do you have $(1,2)R(3,4)$? What about $(3,4)R(1,2)$? What does that tell you? – almagest Apr 27 '16 at 14:16
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Not symmetric. It's just antisymmetry that's got me confused. – rainbow Apr 27 '16 at 14:17
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Ok, so suppose $(a,b)R(c,d)$ and $(c,d)R(a,b)$ are both true. What does that tell you? – almagest Apr 27 '16 at 14:18
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...Not antisymmetric? – rainbow Apr 27 '16 at 14:22
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What does antisymmetric mean? It means that if $(a,b)R(c,d)$ and $(c,d)R(a,b)$ then $(a,b)=(c,d)$. Is that true here? – almagest Apr 27 '16 at 14:23
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That's exactly what I'm confused about, though. I don't quite get antisymmetry. – rainbow Apr 27 '16 at 14:25
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So from what I understood it's antisymmetric then? I'm new to this, sorry. – rainbow Apr 27 '16 at 14:37
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You are correct! Now you can enter your solution as an answer! – almagest Apr 27 '16 at 14:38
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Haha, alrighty then. Thank you very much. :) – rainbow Apr 27 '16 at 14:39