Hi everyone,

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

I started with the following expression: (A U B U C) ∩ (AB U BC U AC)

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

(A U B U C) ∩ ( (AB) ∩ (BC) ∩ (AC))
(A U B U C ) ∩ ( (A U B) ∩ (B U C) ∩ (A U C)
(A U B U C ) ∩ ( (A U B) ∩ (B U C) ∩ (C U A))

(A U B U C) ∩ (A U B) ∩ (B U C) ∩ (C U A)

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!