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Let the (family of sets A) = {A[tex]_{\alpha}:\alpha \in \Delta}[/tex] be a family of sets and let B be a set. Prove that [tex]B \ \cup (\bigcap_{\alpha \in \Delta} A_{\alpha})\subseteq \bigcap_{\alpha \in \Delta} (B \cup A_{\alpha})[/tex]

Don't know how to do this. Trying to get any help possible. We had a similar problem as follows:

Let the (family of sets A) = {A[tex]_{\alpha}:\alpha \in \Delta}[/tex] be a family of sets and let B be a set. Prove that [tex]B \ \cup \bigcap_{\alpha \in \Delta} A_{\alpha} = \bigcap_{\alpha \in \Delta} (B \cup A_{\alpha})[/tex]

To prove this we used:

[tex]x \in \ B \ \cup \ \bigcap_{\alpha \in \Delta} A_{\alpha} \ iff \ x \in B \ or \ x \in A_{\alpha} \ for \ all \ \alpha \ iff \ x \in \bigcap_{\alpha \in \Delta} (B \cup A_{\alpha})[/tex]

Any comments. Is this the same concept?