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I am told A(B ∩ C) ≠ AB ∩ AC I am unsure as to why they are not equal. Using examples and following them I am unable to show that they are not.

e.g Let A = {m} B = {s, p} C = {p, r}

A(B ∩ C) = A{p} = {mp}

AB ∩ AC = {ms, mp} ∩ {mp, mr} = {mp}

Have I made a mistake here?

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