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Midterm Practice: Could some verify my proof

  1. May 28, 2005 #1
    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?
     
    Last edited: May 28, 2005
  2. jcsd
  3. May 28, 2005 #2

    mathman

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    Science Advisor
    Gold Member

    It looks fine to me.
     
  4. May 28, 2005 #3
    Hallelujah!
     
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