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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
Can you check and see if I did my prove correctly? Please let me know in the answer!!
Direction:
Use element argument to prove number 11. Assume that all sets are subset of a universal of U
Transcribed Image Text:tor all set s ArBand C, AnCB-c)<(AnB)- (ANC)
Proof
het A,B and C
be
any sets. Let xe An(B-c)
Xe A and xe (B-c) bay definition of intersection
X E A
and (xE B`and x¢ c) bu definctiun of
Set difforence .
Thus *ETA n B) biy definitioni of intersection and
in additim , x ¢ (A nc).
Theretore
X € (AnB) - (Anc) by definiturm of
Set difference .
Hence ,
A n (B-C) E (AnB) - (Anc) by definition
of sub sets.
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