Question

Show that if A CB, then A = B ( B A ). Show that if A C B, then A U (B \ A) = B. Show, by example, that for sets A, B, and C, AN B = An C does not imply B = C.

Answer 1

Answer: If A ⊂ B, then A = B \ ( B \ A)

ok, when you do B \ A, you are subtracting all the elements in A∩B from B. So the only elements remaining are those who aren't in A.

If we subtract this of B again, we are subtracting of B all the elements that aren't in A, so the only elements remaining are those who belongs in A.

If A ⊂ B then A U (B \ A) = B.

Again, when you do B \ A you are extracting all the elements that belongs to the A∩B from B. So you are extracting al the elements from A. and when you add all the elements of A again, then you recuperate B.

if AnC = AnC does not imply that B = C.

if A = {1,2}, B = {1,2,3,4,5} and C = {1,2,3}

then AnC = {1,2} and AnB = {1,2} but B and C are different.