Order the 11 following sentences so that they form a logical proof of the statement below using double inclusion to prove the equality, and direct method in both cases: For any non-empty sets B and D Order B\D=BnD Sentences a. Letz € BD b. By definition, z € Band z E D C. E BOD d. Hence, z € B and a D e. r € B\D f. Hence, a E B and a € D g. Let z E BnD. h. Thus, B D C BnD. i. Therefore, B\D=BnD. j. Then, Bn DC BD. k. By definition, 2 E B and a D
Order the 11 following sentences so that they form a logical proof of the statement below using double inclusion to prove the equality, and direct method in both cases: For any non-empty sets B and D Order B\D=BnD Sentences a. Letz € BD b. By definition, z € Band z E D C. E BOD d. Hence, z € B and a D e. r € B\D f. Hence, a E B and a € D g. Let z E BnD. h. Thus, B D C BnD. i. Therefore, B\D=BnD. j. Then, Bn DC BD. k. By definition, 2 E B and a D
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.4: Binary Operations
Problem 14E: Assume that is a binary operation on a non empty set A, and suppose that is both commutative and...
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