If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C, then:

A = B A = C B = C $A ∩ B=\phi$

B = C

$A ∩ B-A ∩ C=\phi$ and $A ∪ B - A ∪ C=\phi$ $A ∩ (B-C)=\phi$ and $A ∪ (B - C)=\phi$ Both possible if B = C