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 tor all set s ArBand C, AnCB-c)<(AnB)- (ANC)Proofhet A,B and Cbeany sets. Let xe An(B-c)Xe A and xe (B-c) bay definition of intersectionX E Aand (xE B`and x¢ c) bu definctiun ofSet difforence .Thus *ETA n B) biy definitioni of intersection andin additim , x ¢ (A nc).TheretoreX € (AnB) - (Anc) by definiturm ofSet difference .Hence ,A n (B-C) E (AnB) - (Anc) by definitionof sub sets.

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Math

Advanced Math

Direction

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

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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