Determine which of the three properties (reflexive, symmetric, and transitive) apply to ea...

Determine which of the three properties (reflexive, symmetric, and transitive) apply to each relation.

(a) Let R be the relation on N given by xRy iff x divides y.

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(b) Let X be a set and let R be the relation "⊆" defined on subsets of X

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(c) Let S be the set of people in the school. Define R on S by xRy iff  "x likes y."

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(d) Let R be the relation {(l, 1), (1,2), (2,2), (1,3), (3,3)} on the set {1,2,3}.

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(e) Let R be the relation on  given by xRy iff x – y is rational.

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(f) Let R be the relation on  given by xRy iff x – y is irrational.

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(g) Let R be the relation on  given by xRy iff (x–y )2<0.

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(h) Let R be the relation on  given by xRy iff |x – y|≤ 2.