SOLUTION: Proof that (AUB)UC= AU(BUC)

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Question 1173564: Proof that (AUB)UC= AU(BUC)
Answer by ikleyn(52855) About Me  (Show Source):
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If an element x belongs to the left hand side, then it belongs to one of the sets A, B or C.

Hence, it belongs to the set in the right hand side.



In opposite, if an element y belongs to the right hand side, then it belongs to one of the set A, B or C.

Hence, it belongs to the set in the left hand side.



It proves that the left hand side set is the same as the right hand side set,

and the statement is proved.