Complement of a setThis lesson will explain how to find the complement of a set. We will start with a definition Given a set A, the complement of A is the set of all element in the universal set U, but not in A. We can write A^{c} You can also say complement of A in U Example #1. Take a close look at the figure above. d and f are in U, but they are not in A. Therefore A^{c} = {d, f} 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 U, but not in A A = { a, b, c} U = { a, b, c, d, f} Example #2. Let B = {1 orange, 1 pinapple, 1 banana, 1 apple} Let U = {1 orange, 1 apricot, 1 pinapple, 1 banana, 1 mango, 1 apple, 1 kiwifruit } Again, we show in bold all elements in U, but not in B B^{c} = {1 apricot, 1 mango, 1 kiwifruit} Example #3. Find the complement of B in U B = { 1, 2, 4, 6} U = {1, 2, 4, 6, 7, 8, 9 } Complement of B in U = { 7, 8, 9} Example #4. Find the complement of A in U A = { x / x is a number bigger than 4 and smaller than 8} U = { x / x is a positive number smaller than 7} A = { 5, 6, 7} and U = { 1, 2, 3, 4, 5, 6} A^{c} = { 1, 2, 3, 4} Or A^{c} = { x / x is a number bigger than 1 and smaller than 5 } The graph below shows the shaded region for the complement of set A This ends the lesson about the complement of a set. 




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