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Unformatted text preview: Answer key of First Midterm Examination, Math 61, Version 2 1. Let X be an n element set. How many ordred pairs ( A,B ) of subsets of X satisfy A ⊆ B ⊆ X . Answer 3 n . Read Example 1.6 page 110 in the text (UCLA edition) or Example 6.1.6 (page 223) in the original 6th edition. 3 . Compute the following numbers, explain how you get the answer and write your answer in the following boxes as indicated: a. 4 b. 50 c. 16 d. 144 e. 8 a. In the set of seven bit strings, x = ( x 1 x 2 ...x 7 ) and y = ( y 1 y 2 ...y 7 ) are defined to be related if x 1 = y 1 and x 7 = y 7 . How many equivalence classes are there? Each equivalence class is determined by the first and the last bit: 2 2 = 4 equivalence classes. b. In a seven person committee made of persons A,B,C,D,E,F,G , in how many ways can we select a chairperson, secretary and treasurer if either A or B must be chairperson and C cannot be a treasurer?...
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- Spring '09