9. Which of the following are true for all sets A, B, and C. If the statement is true, prove it by showing each is a subset of the other. If not, provide a counterexample. (i) ∅ × A = ∅ (j) (A \ B) ∪ (B \ C) = A \ C. (k) (A \ B) ∩ (A \ C) = A \ (B ∪ C)
9. Which of the following are true for all sets A, B, and C. If the statement is true, prove it by showing each is a subset of the other. If not, provide a counterexample. (i) ∅ × A = ∅ (j) (A \ B) ∪ (B \ C) = A \ C. (k) (A \ B) ∩ (A \ C) = A \ (B ∪ C)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.CR: Chapter 12 Review
Problem 3CR
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9. Which of the following are true for all sets A, B, and C. If the statement is true, prove it by showing each is a subset of the other. If not, provide a counterexample.
(i) ∅ × A = ∅
(j) (A \ B) ∪ (B \ C) = A \ C.
(k) (A \ B) ∩ (A \ C) = A \ (B ∪ C)
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