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Math Help - Cartesian product

  1. #1
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    Cartesian product

    Prove: If  A \subset C and  B \subset D, then  A \times B \subset C \times D.
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  2. #2
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    Quote Originally Posted by onemore View Post
    Prove: If  A \subset C and  B \subset D, then  A \times B \subset C \times D.
    Note that  A \times B = \{ (a,b) : a \in A, b \in B \} and  C \times D = \{ (c,d) : c \in C, d \in D \}

    So, pick an element in  A \times B , say (a,b). You want to show that it is in  C \times D .

    Now, as  a \in A \subset C , we have that  a \in C

    Can you take it from here?
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