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

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

Advanced Engineering Mathematics
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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The following is a proof that ``For all sets A and B, P(A^ B) ≤ P(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 SEP(ANB). By definition of power sets, then SCAN B.. Since An BCA, then . Similarly, since An BCB, then and so, Hence, by definition of Therefore, P(ANB) ≤ P(A) ~P(B). ,S ♦ P(A)^P(B). Q.E.D. *Note here that in the choices, P(A) represents the power set of A. and so,
Transcribed Image Text:The following is a proof that ``For all sets A and B, P(A^ B) ≤ P(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 SEP(ANB). By definition of power sets, then SCAN B.. Since An BCA, then . Similarly, since An BCB, then and so, Hence, by definition of Therefore, P(ANB) ≤ P(A) ~P(B). ,S ♦ P(A)^P(B). Q.E.D. *Note here that in the choices, P(A) represents the power set of A. and so,
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