Let A, B, C, and D be the following sets: A = {red, blue, green, purple} B = {re

Question

Let A, B, C, and D be the following sets: A = {red, blue, green, purple} B = {red,red, green} C = {red, {green},red, {red, green}, {green, green,red}} D = {blue, blue, blue, green, green, purple} Let the universal set for A,B, C, D be defined by:

U = {red, blue, purple, green} P({red, blue, purple, green}) Provide the answer to the following questions about the above sets.

1. Does there exist a partition of A by 3 sets? If yes, provide one. If no, explain.

2. Does there exist a partition of D by 4 sets? If yes, provide one. If no, explain

Explanation / Answer

1. A1={red, blue}, A2={green}, A3={purple} Notice that A1, A2 andA3 are pair wise disjoint (no common elements) and their union is A. Therefore A1, A2 andA3 form a partition of A.

2. No. There does not exist a partition of D by 4 sets. Because D it self contains only 3 distinct elements.

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