Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Let P = P(A) be the power set of A. Let R be the relation on P defined by: For all X, Y EP, X RY if and only if XUY| ≤ |XU {1,2}|. (a) Is R reflexive? symmetric? antisymmetric? transitive? Prove your answers. (b) How many SE P are there so that S R {3}? Explain. (c) How many SP are there so that {3} RS? Explain.

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A: R1=1, 1, 2, 2  &  R2=1, 1, 1, 2 are the relations defined on set A=1, 2.

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Q: 1. Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9}. Let P = P(A) be the power set of A. Let R be the relation on…

A: (a) For any X ∈ P,            | X ∪ X | = |X|           | X ∪ {1, 2} | = |X| + |{1, 2}| - |X ∩ {1,…

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A: Solution:

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A: See the attachment

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Q: 4), (4,2)} Draw the diagraph of R

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A: Solution:

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A: We will prove the given statement.