Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Question

answer by functions and relations:

 

1.Define a function f ∶ P(Z) → P(Z) that sends a subset X ⊆ Z to its compliment Xc.
Prove or disprove that this function is a bijection. If it is a bijection, find its inverse;
if it is not, explain why.

2.Let R and S be equivalence relations on a set X. Prove or disprove the following:
(a) R ∩ S is an equivalence relation on X
(b) R ∪ S is an equivalence relation on X

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