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3.* Show that (A \ B) \ C = A \ (BUC). Is (A \ B)\C = A\ (B\C)? 4.* If A and B are sets, we define their symmetric difference as

3.* Show that (A \ B) \ C = A \ (BUC). Is (A \ B)\C = A\ (B\C)? 4.* If A and B are sets, we define their symmetric difference as

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.1: Postulates For The Integers (optional)
Problem 26E: Prove that the cancellation law for multiplication holds in Z. That is, if xy=xz and x0, then y=z.
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3.* Show that (A \ B) \ C = A \ (BUC). Is (A \ B)\C = A\ (B\C)? 4.* If A and B are sets, we define their symmetric difference as ΑΔΒ = Α } Β) υ (B] Α) . Prove that AAB=Ø if and only if A = B. (Hint: remember that to prove an “if and only if" statement, you need to prove two implications, one in each direction)
Transcribed Image Text:3.* Show that (A \ B) \ C = A \ (BUC). Is (A \ B)\C = A\ (B\C)? 4.* If A and B are sets, we define their symmetric difference as ΑΔΒ = Α } Β) υ (B] Α) . Prove that AAB=Ø if and only if A = B. (Hint: remember that to prove an “if and only if" statement, you need to prove two implications, one in each direction)
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