One other operation in set theory is called set difference. Given two sets A and B taken from some universe U, then A minus B, written AB is the set of all elements that are in A but not in B.
Example.
U = { 1,2,3,4,5,6}
A = { 1,4,5,6}
B = {1,3,4}
AB = {5,6}
Combining operations allows us to solve problems such as those below.
U = {1,2,3,4}
A = { 1,2}
B = { 2,3}
Find (A ½B)’
The part in parentheses is done first giving us the number 2. (A ½ B)’ = { 1,3,4} since these are the elements in the universe which are not in the intersection of (A½ B.)
Try the following:
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Find:
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Solutions:
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Additional exercises can be developed by the teacher to test understanding for set concepts presented in this unit. One such exercise is shown below.
Prove that AB = A ½B’
Solution:
AB = A. B’ is A which makes A ½B’ also equal to A. Since both sides of the equation equal set A we have proven that A B = A ½B’.
