Please answer last three question e,c,d. Last three questions. You are given the

Question

Please answer last three question e,c,d. Last three questions.

You are given the set A = {a, b, c}. a. Find all subsets of the seti4 (that is, find the power set of A). b. Is the power set of A a partition of A? If not, why not? c. Find all partitions of the set A. d. For each partition of A, create the relation induced by the partition. e. For each relation, find [a]_R =, [b]_R =, [c]_R =. c. What partition of A' = {a, b, c, d} creates the equivalence relation with the fewest elements? d. What partition of A' = {a, b, c, d} creates the equivalence relation with the most elements?

Explanation / Answer

A={a b c}

powerset of A is all the subsetsb}

=( {a}, {b}, {c}, {},{a,b}, {b,c}, {c,a},{a,b,c} )

The power set of A is a partition of A

partitions of set A are ({a} {b,c})

({b} {a,c})

({c} {c,a})

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