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lesson1 Maki - a ab b c c Lesson 1 Written Assignment...

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a b c d e a b c d e Lesson 1 Written Assignment Finite Mathematics Maki Section 1.1 (pages 9-11) 2. With R , S , and T defined as in Exercise 1, decide whether each of the following assertions is correct. (a) R T This assertion is correct. (b) ( R S ) T This assertion is incorrect. (c) c S T This assertion is correct. 6. Let U = {1, 2, 3, 4, 5} be a universal set with subsets A = {2, 4} and B = {1, 5}. List the elements in each of the following sets. (a) A′ A′ = {1, 3, 5} (b) A' B' A' B' = {3} (c) A B A B = {1, 2, 4, 5} (d) ( A B ) ' ( A B ) ' = {3} 10. Let U = { x , y , z , 1, 2, 3}, A = { y , z , 2}, B = { y , 1, 2}, and C = { x , 3}. List the elements in each of the following sets. (a) A B = { y , z , 1, 2} (b) B C = (c) A' = { x , 1, 3} (d) ( A B ) ∩ ( B C ) = { y , 1, 2} (e) ( B A' ) ∩ C' = {1}. 12. Let sets R , S , and T be defined as follows: R = { x : x lives in the residence halls at Gigantic Sate University} S = { x : x is a student at Gigantic State University} T = { x : x is an employee of Gigantic State University} Describe in words each of the following sets. (a) S R This set consists of students at Gigantic State University who live in residence halls at Gigantic State University. (b) S T This set consists of the people at Gigantic State University who are either students or employees at Gigantic State University. (c) ( S T ) R This set consists of the people at Gigantic State University who are both students and employees at Gigantic State University and the people at Gigantic State University who live in residence halls. 14. Let X and Y be sets with a X and b Y . Is it always true (yes or no) that { a , b } X Y ? Yes, always true. That { a , b } X Y ? No, not always true. 18. Let U = { w , x , y , z }. Find examples of subsets A and B of U which satisfy the stated condition.
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(a) A B = A True if A = { w } and B = { w }. (b) A B = A True if A = { w } and B = { w }. 26. With A and B as in Exercise 25, find ( A × A ) ∩ ( B × B ). ( A × A ) = {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c)} ( B × B ) = {(a, a), (a, b), (a, d), (b, a), (b, b), (b, d), (d, a), (d, b), (d, d)} ( A × A ) ∩ ( B × B ) = {(a, a), (a, b), (b, a), (b, b)} Section 1.2 (pages 17-19) 2a. Let A , B , and C be subsets of a set U . Which of the following Venn diagrams illustrates the set ( A B' ) B ? Venn diagram a above is correct. 2b. Let A , B , and C be subsets of a set U . Which of the following Venn diagrams illustrates the set A B C' ? Venn diagram c above is correct.
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2c. Let A , B , and C be subsets of a set U . Which of the following Venn diagrams illustrates the set A' ( B C )?
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