Question

for any sets A,B,C, prove that A∩(B⊕C)=(A∩B)⊕(B∩C)

for any sets A,B,C, prove that A∩(B⊕C)=(A∩B)⊕(B∩C)

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Answer #1

Means

So that or (by definition of symmetric difference)

So that or

Which means or

Combining these, we get (the left side is not B but A in the last set as can be checked on some online reference such as wikipedia, image below for reference:)

Thus, we have

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