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Unformatted text preview: English. Region (c) contains all students taking English but not mathematics. Region (d) contains all students taking neither mathematics nor English. Example 5 In a survey of 110 college freshmen that investigated their high school backgrounds, the following information was gathered: 25 took physics, 45 took biology, 48 took mathematics, 10 took physics and mathematics, 8 took biology and mathematics, 6 took physics and biology, 5 took all three subjects. a. How many students took biology but neither physics nor mathematics? b. How many took physics, biology, or mathematics? c. How many did not take any of the three subjects? Cartesian Products One way to produce a set from two sets is by forming pairs of elements of one set with the elements of another set in a specific way. Suppose a person has three pairs of pants, P = {blue, green, white}, and two shirts, S = {blue, red}. According to the Fundamental Counting Principle, there are 3 • 2 = 6 possible ways to pair an element from set P with an element from set S, forming a set of ordered pairs. Because the first component in each pair represents pants and the second component in each pair represents shirts, the order in which the components are written is important. Equality for ordered pairs: (x, y) = (m, n) if, and only if, the first components are...
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