\ begin {ecuation*}\ begin {split} A\ cap (B-C) &=A\ cap (B\ cap C^c)\\ & = (A\ cap B\ cap A^c)\ copa (A\ cap B\ cap C^c)\\ & = (A\ cap B)\ cap (A^c\ copa C^C)\ & = (A\ cap B) cap\ (A\ copa C) ^c\\ & ...\ begin {ecuation*}\ begin {split} A\ cap (B-C) &=A\ cap (B\ cap C^c)\\ & = (A\ cap B\ cap A^c)\ copa (A\ cap B\ cap C^c)\\ & = (A\ cap B)\ cap (A^c\ copa C^C)\ & = (A\ cap B) cap\ (A\ copa C) ^c\\ & = (A-B)\ cap (A-C)\ quad\ cuadrado\\ final {split}\ text {.} \ end {ecuación*} \ begin {ecuation*}\ begin {split} A- (B\ copa C) & = A\ cap (B\ copa C) ^c\\ & =A\ cap (B^c\ cap C^c)\\ & = (A\ cap b^c)\ cap (A\ cap c^c)\\ & = (A-B)\ cap (A-C)\ quad\ square\ end\ {dividir}\ texto {.} \ end {ecuación*}
