Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor

    It looks fine to me.
  4. May 28, 2005 #3
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook