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.

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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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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