For all sets A, B, and C. Assuming each is a subset of a universal set U a)Is the following true? (A-B)∩ (C-B) = A- (B ∪C) b)Find a counterstatement to (a) 2/16/2014 | Daniel from Ocala, FL | 1 Answer | 0 Votes Mark favorite Subscribe Comment
For any set A let A'=complement of A. Definition: A-B=A∩B' . De Morgan's Law: (B∪C)'=B'∩C' Now we begin (A-B)∩C-B=A∩B'∩C∩B'=A∩C∩B'=A∩B'∩C A-(B ∪C)=A∩(B ∪C)'=A∩B'∩C' The two sets are disjoint! One is a subset of C, the other of C' 2/16/2014 | Michael F. Comment