You are given the set A = {a, b, c}. 8a. Find all subsets of the set A (that is,

Question

You are given the set A = {a, b, c}. 8a. Find all subsets of the set A (that is, find the power set of A). 8b. Is the power set of A a partition of A? If not, why not? 8c. Find all partitions of the set A. 8d. For each partition of A, create the relation induced by the partition. 8e. For each relation, find [a]_R =, [b]_R =, [c]_R = 8c. What partition of A' = {a, b, c, d} creates the equivalence relation with the fewest elements? 8d. What partition of A' = {a, b, c, d} creates the equivalence relation with the most elements?

Explanation / Answer

(As per Chegg policy only four subquestions will be answered. Please post the remaining in another question)

A = {a,b,c}

a. Subsets are {}, {a}, {b}, {c}, {a,b}, {b,c}, {a,c}, {a,b,c}

b. Power set of A is not a partition of A as the same elements are repeated in more than one subset.

c and d. The partititions with their relations are

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

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

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

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

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

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