Difference of setsThis lesson will explain how to find the difference of sets. We will start with a definition Definition: Given set A and set B the set difference of set B from set A is the set of all element in A, but not in B. We can write A − B Example #1. Take a close look at the figure above. Elements in A only are b, d, e,g. Therefore, A − B = { b, d, e, g} Notice that although elements a, f, c are in A, we did not include them in A − B because we must not take anything in set B. Sometimes, instead of looking at a the Venn Diagrams, it may be easier to write down the elements of both sets Then, we show in bold the elements that are in A, but not in B A = {b, d, e, g, a, f, c} B = { k, h, u, a, f, c} Example #2. Find B − A Notice that this time you are looking for anything you see in B only Elements that are in B only are shown in bold below Let A = {1 orange, 1 pinapple, 1 banana, 1 apple} Let B = {1 orange, 1 apricot, 1 pinapple, 1 banana, 1 mango, 1 apple, 1 kiwifruit } B − A = {1 apricot, 1 mango, 1 kiwifruit} Example #3. Find A − B B = { 1, 2, 4, 6} A = {1, 2, 4, 6, 7, 8, 9 } What I see in A that are not in B are 7, 8, and 9 A − B = { 7, 8, 9} Example #4. Find B − A A = { x / x is a number bigger than 6 and smaller than 10} B = { x / x is a positive number smaller than 15} A = {7, 8, 9} and B = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14} Everything you see in bold above are in B only. B − A = {1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14} The graph below shows the shaded region for A − B and B − A This ends the lesson about the difference of sets. 




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