How do I prove that: A⊆B⊆C ⇔ A∪B=B∩C

Answer 1

Draw a Venn Diagram

3 circles, C the largest with B inside and A inside B

A UB = B

B intersection C = B

so

AUB = BintersectionC

that's half the proof, the righward arrow, if left side then the right side

work backwards for the reverse arrow, if right side then left side