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. For all set s A,Band C, An(B-c)C(AnB)-(Anc)Proof:het A, B and Csets. Let xE An(B-c)beanyXE A and xe (B-c) by definition of intersectionX E Aand (aE Band x¢ c) by defntin ofSet difference .Thus *E(A n B) biy definitioni of intersecton andin additimX € (A nc) by defimtion of set differen ce,TheretoreX € (AnB) - (Anc) by definitun ofSet difference .Hence,A n (B-C) E (ANB) - (Anc) by definitionof sub sets.

Proof is almost correct but here it is some modifications of the details explanation.

Answered: For all sets ABand C, ANCB-c)

Math

Advanced Math

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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Question

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.

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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