The following is a proof that "For all sets A and B, P(An B) CP(A) P(B)". Fill in the blanks. Proof: Suppose that A and B are any sets, and suppose that S is a set such that definition of power sets, then SCAN B.. Since An BCA, then + and so, + and so, Similarly, since An BCB, then + S + P(A) P(B). +. By Hence, by definition of Therefore, P(An B) CP(A) P(B). Q.E.D. *Note here that in the choices, P(A) represents the power set of A.
The following is a proof that "For all sets A and B, P(An B) CP(A) P(B)". Fill in the blanks. Proof: Suppose that A and B are any sets, and suppose that S is a set such that definition of power sets, then SCAN B.. Since An BCA, then + and so, + and so, Similarly, since An BCB, then + S + P(A) P(B). +. By Hence, by definition of Therefore, P(An B) CP(A) P(B). Q.E.D. *Note here that in the choices, P(A) represents the power set of 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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