Let U = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14}, A = {6, 8, 10, 12}, B = {9, 13}, and C = {6, 9, 12, 13, 14}. List all the members of each of the sets. (a) (A �¿ B) �¿ C , (b) A �¿ B �¾ C
Let U = {8, 9, 10, 11, 12, 13, 14}, A = {8, 9, 10, 11}, B = {8, 9, 12, 13}, and C = {10, 12, 14}. List all the members of the given set. (Enter your answers as a comma-separated list.)
(A ∪ B) ∩ C
To solve this, we need to understand the concepts of set operations. There are three basic set operations – union, intersection, and complement – and some derived operations such as difference and symmetric difference.
Let's break down the problem step by step:
(a) To find (A �¿ B) �¿ C:
1. First, we find the intersection of A and B: A �¿ B = {6, 8, 10, 12} ∩ {9, 13} = {} (empty set because there are no common elements).
2. Now, we take the result from step 1 and intersect it with C: {} �¿ C = {} (empty set).
Therefore, (A �¿ B) �¿ C = {}.
(b) To find A �¿ B �¾ C:
1. First, we find the difference between A and B: A - B = {6, 8, 10, 12} - {9, 13} = {6, 8, 10, 12} (as all elements in A are distinct from B).
2. Next, we find the symmetric difference between the result from step 1 and C: {6, 8, 10, 12} �¾ C = {6, 8, 10, 12} ∆ {6, 9, 12, 13, 14} = {8, 9, 10, 13, 14} (symmetric difference includes elements that are in either of the two sets, but not in the intersection).
Therefore, A �¿ B �¾ C = {8, 9, 10, 13, 14}.