(adsbygoogle = window.adsbygoogle || []).push({}); Midterm Practice: Could someone verify my proof

A sample question that I tried proving is:

Formally show that [tex]A \subseteq B,~then~A \cap C \subseteq B \cap C[/tex]

My Proof:

Suppose [tex]x \in A \cap C[/tex]. Then by definition of intersection, [tex]x \in A~and~x \in C[/tex]. But as [tex]A \subseteq B,~then~x \in B[/tex]. Hence, [tex]x \in B \cap C[/tex]. And therefore, [tex]A \cap C \subseteq B \cap C[/tex].

Is there anything that I've missed? Is this even right?

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# Midterm Practice: Could some verify my proof

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