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Math Help - need help with 2 proofs

  1. #1
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    need help with 2 proofs

    Prove: If |A| = n and A is equinumerous to B, then |B| = n

    Prove: Let A and B be finite sets. Conjecture a formula for |A U B| in the case that A n B doesn't equal the empty set
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  2. #2
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    Quote Originally Posted by dbhakta View Post
    Prove: If |A| = n and A is equinumerous to B, then |B| = n
    If |A|=n it means there is a bijection \theta : A\mapsto n, and |A|=|B| means there is a bijection \eta: A\mapsto B. Thus, the mapping \theta \circ \eta^{-1} will be a bijection from B to n.

    Prove: Let A and B be finite sets. Conjecture a formula for |A U B| in the case that A n B doesn't equal the empty set
    If |A|=n and |B|=m then |A\cup B| \leq n+m and we have equality when A\cap B=\emptyset.
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