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$(i) X\cap(\bigcup\limits_{n=1}^\infty A_n) = \bigcup\limits_{n=1}^\infty (X\cap A_n)$

$(ii) X\cup(\bigcap\limits_{n=1}^\infty A_n) = \bigcap\limits_{n=1}^\infty (X\cup A_n)$

Any suggestions on how to approach this?

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    Use the same basic ‘element-chasing’ approach that I used in [this answer](http://math.stackexchange.com/a/216164/12042) to your similar question about DeMorgan’s laws.2012-10-18

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