Hi everyone,

I'm trying to simplify a set notation and am stuck at certain point.

I started with the following expression: (AUBUC) ∩ (A’BUB’CUAC’)’

I started by moving the negation inside with De Morgan's and ended up with:

(AUBUC) ∩ ( (A’B)’ ∩ (B’C)’ ∩ (AC’)’)

(AUBUC) ∩ ( (AUB’) ∩ (BUC’) ∩ (A’ UC)

(AUBUC) ∩ ( (AUB’) ∩ (BUC’) ∩ (CUA’))

(AUBUC) ∩ (AUB’) ∩ (BUC’) ∩ (CUA’)

At this point, I'm not sure how to proceed further... is there something I can do with the A / B / C inside of (A U B’) ∩ (B U C’) ∩ (C U A’) so that I can use absorption with (A U B U C)? Or should I take out either A or B or C individually with Distributivity, and hope to have a case where (X U Y U Z) ∩ = (X U Y)?

I'd greatly appreciate any guidance that could be provided - thanks so much!