Let A and B be subsets of some universal set U. Prove or disprove that?

Question

(A u B) - (A n B) = (A - B) u (B - A)

Answer 1

I'll use ' to indicate the complement.
LHS = (A u B) - (A n B)
= (A u B) n (A n B)'
= (A u B) n (A' u B')
= (A n (A' u B')) u (B n (A' u B'))
= ((A n A') u (A n B')) u ((B n A') u (B n B'))
= (∅ u (A-B)) u ((B-A) u ∅)
= (A-B) u (B-A)
= RHS.

Answer 2

the two statements are actual. I fairly have converted them into extra undemanding language however the evidence looks too intuitive to completely clarify. a)eliminate out all contributors of A which at the instant are not in B and the rest would be in the two A and B. b)Any member that's in A or B yet no longer in the two is the two A yet no longer B or B yet no longer A.

Answer 3

its true.. scarlet has proved it mathematically.. u can do it using venn diagram also.. and (AuB) - (AnB) = (A-B) u (B-A) is called the symmetric difference of the sets A and B

Answer 4

(A u B) - (A n B)=(A u B)n(A'uB')=((A u B)nA')u((A u B)nB')=
[(AnA')u(BnA')]u[(AnB')u(BnB')]=(BnA')u(AnB')=(B-A)(A-B)
By using the facts An(BuC)=(AnB)u(AnC), Au(BnC)=(AuB)n(AuC), A-B=AnB', BnB'=empty, (AnB)'=(A'uB')
(AuB)'=(A'nB')