Question: a) Let X = {1,2,3,4,5}. On Y = P(X) {} (= all non-empty subsets of {1,2,3,4,5} ) define a relation by A R B if

a)Let X = {1,2,3,4,5}. On Y = P(X) {} (= all non-empty subsets of {1,2,3,4,5} ) define a relation by

A R B if and only if A B

Which of the properties of an equivalence relation hold for R, and which ones fail?

b) On the same set Y define a relation byA R B if and only if every number in A is smaller or equal to some number in B.

Which of the properties of a partial order hold for R, and which ones fail?

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