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Determine if the binary relation <= is a partial order on A in the following cases: (a)...

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Advance Math

Determine if the binary relation <= is a partial order on Ain the following cases:

(a) A = N × N and (a1, b1) (a2, b2) ? a1 <= a2 for (a1,b1),(a2, b2) ? A

(b) X = {1, 2, 3, 4}, A = P(X) and a <= b ? #a <= #b fora, b ? A (Here #a denotes the number of elements in the set a)

(c) A = N and a <= b ? ?k ? N : a^k = b

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