For all sets ABand C, ANCB-c)
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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Can you please check my prove and please let me know if I did it correctly. Thank you!
One more question , is x is not in (A and B ) by definition of set different or set of intersection?
Directions for the problem: use element argument to prove number 11. Assume that all sets are subset of a universal of U.

Transcribed Image Text:For all set s A,Band C, An(B-c)C(AnB)-(Anc)
Proof:
het A, B and C
sets. Let xE An(B-c)
be
any
XE A and xe (B-c) by definition of intersection
X E A
and (aE Band x¢ c) by defntin of
Set difference .
Thus *E(A n B) biy definitioni of intersecton and
in additim
X € (A nc) by defimtion of set differen ce,
Theretore
X € (AnB) - (Anc) by definitun of
Set difference .
Hence,
A n (B-C) E (ANB) - (Anc) by definition
of sub sets.
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