As an example for which the equality holds, let A = {1, 2, 3}, B = {2}, and C = {3}. Then on the left side,
A - (B U C) = {1, 2, 3} - ({2} U {3})
… = {1, 2, 3} - {2, 3}
… = {1}
and on the right,
(A - B) ∩ (A - C) = ({1, 2, 3} - {2}) ∩ ({1, 2, 3} - {3})
… = {1, 3} ∩ {1, 2}
… = {1}
