Mark each statement True or False. Justify each answer.(a) If  is a partition of set S, th...

Mark each statement True or False. Justify each answer.

(a) If  is a partition of set S, then we can obtain a relation R on S by defining x Ry iff x and y are in the same piece of the partition.

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(b) In any relation R on a set S, we always have xRx for all x ∈ S.

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(c) If R is a relation on S, then {y ∈ S; yRx} determines a partition of S.

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(d) If  is a partition of S and x ∈ S, then x ∈ A for some A ∈.