Disprove the following statement by finding a counterexample.
For all sets A, B, and C, A ? (B ? C) ? (A ? B) ? C.
Counterexample: Let A = {1}, B = {2}, and C = {2}. Then A?(B?C) = {1}?({2}?{2}) = {1} ? {2} = {1, 2},
and (A ? B) ? C = ({1} ? {2}) ? {2} = {1, 2} ? {2} = {2}. Thus 1 ? A ? (B ? C) whereas 1 /?
(A ? B) ? C. Therefore, A ? (B ? C) * (A ? B) ? C.
[This is one counterexample among many.]
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