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Math Help - proof about subsets and intersections

  1. #1
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    proof about subsets and intersections

    If A is a subset of B and C is a subset of D, then A intersect C is a subset of B intersect D.

    Please any help in proving this conditional would be much appreciated
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  2. #2
    Senior Member Danneedshelp's Avatar
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    Quote Originally Posted by leinadwerdna View Post
    If A is a subset of B and C is a subset of D, then A intersect C is a subset of B intersect D.

    Please any help in proving this conditional would be much appreciated
    Suppose that x\in{A\cap\\C}. Then, x\in{A} and x\in{C}. Since A\subset{B}, x\in{B} and, because C\subset{D}, x\in{D} as well. Thus, x\in{B\cap{D}}.
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