2. For an arbitrary set A, the power set P(A) = {X | X C A}, and addition in P(A) defined by X+ Y = (X U Y) - (X n n = (X– Y) U (Y– X) a. Prove that P(A) is a group with respect to this operation of addition. b. If A has n distinct elements, state the order of P(A).
2. For an arbitrary set A, the power set P(A) = {X | X C A}, and addition in P(A) defined by X+ Y = (X U Y) - (X n n = (X– Y) U (Y– X) a. Prove that P(A) is a group with respect to this operation of addition. b. If A has n distinct elements, state the order of P(A).
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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please be as thorough as you can. When finished please provide 2-3 examples. Please.
Transcribed Image Text:2. For an arbitrary set A, the power set P(A) = {X | X S A}, and addition in P(A) defined by
X + Y = (XU Y) - (Xn) = (X- Y)U (Y–X)
a. Prove that P(A) is a group with respect to this operation of addition.
b. If A has n distinct elements, state the order of P(A).
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