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#### MikeLandry

##### New member

- Mar 7, 2013

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Consider any three arbitrary sets A, B and C.

(a) Show that if A ∩ B = A∩ C and A ∪ B = A ∪ C, then B = C.

(b) Show that if A − B = B − A, then A = B.

(c) Show that if A∩B = A∩C = B ∩C and A∪B ∪C = U, then A⊕B ⊕C = U.

For the three proofs so far i have

a) So A intersects C = A intersects B and A union B= A union C.

Let

Similarly, let

b)

A−B=A∩Bc where Bc is the complement of B.

Now if A≠B then (∃x)[x∈A∩Bc or x∈B∩Ac]

for