Hi, I would like some help for the following problems.(adsbygoogle = window.adsbygoogle || []).push({});

please bear with me with my special notation:

I- intersection

U- union

S- universal set

~- complement

I need to prove that: let be A and B two sets. prove

(AUB)I(AI(~B))=A

what I did is:

(AUB)I(AI(~B))

=[(AIB)UA]I[(AIB)U~B]/distribution

=AI[(~BUA)I(~BUB)]

=AI[(~BUA)US)

=AI(~BUA)

=(AI(~B))U(AIA)

=AUA=A //i'm not sure here (AI(~B)) =A

problem 2

Can we conclude that A=B if A,B,C are sets such that

i) AUC = BUC

ii) AIC = BIC

how can I treat this problem?

Thank you for your help

B

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# Homework Help: Proof in Discrete math

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