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Show by simplification

  1. Sep 11, 2006 #1
    Hi,

    with my special notation:
    I- intersection

    Can we prove that:
    (A I B) subset of A by simplification from the rule of inference

    since A I B -->A ??

    If not, please can I have some suggestions?
    B
     
  2. jcsd
  3. Sep 11, 2006 #2

    0rthodontist

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    Science Advisor

    Sort of--that logical rule applies only to logical statements, not directly to sets. It says that you can conclude X from the statement X AND Y. The standard way to prove that [tex]A \cap B \subseteq A [/tex] starts by decomposing it into logical statements.
    Assume [tex]x \in A \cap B[/tex]
    Then [tex](x \in A) \vee (x \in B)[/tex]
    You can finish it
     
  4. Sep 13, 2006 #3
    OK I understand what to do.
    Thank you
     
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