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Math Help - question on sets

  1. #1
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    Question question on sets

    Consider the sets A={x | x=2n, n is natural integer} & B = {y | if y is a natural
    integer and is divisible by 2}. Both the sets A and B seem to signify the same
    thing. Do you agree? Justify your answer in the light of set definition.

    Please help me as i could not solve the question
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  2. #2
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    p \in A \Rightarrow \left( {\exists j \in \mathbb{N}} \right)\left[ {p = 2j} \right] \Rightarrow \left[ {2|p} \right] \Rightarrow p \in B

    q \in B \Rightarrow \left[ {2|q} \right] \Rightarrow \left( {\exists k \in \mathbb{N}} \right)\left[ {q = 2k} \right] \Rightarrow q \in A
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  3. #3
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    could you explain it to me a little

    I could not understand the signs
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  4. #4
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    Quote Originally Posted by Plato View Post
    p \in A \Rightarrow \left( {\exists j \in \mathbb{N}} \right)\left[ {p = 2j} \right] \Rightarrow \left[ {2|p} \right] \Rightarrow p \in B [/tex]
    If p is in A then there is a natural number, j, and p=2j; then 2 divides p so p belongs to B.


    Quote Originally Posted by Plato View Post
    q \in B \Rightarrow \left[ {2|q} \right] \Rightarrow \left( {\exists k \in \mathbb{N}} \right)\left[ {q = 2k} \right] \Rightarrow q \in A
    If q is in B then because 2 divides q there is a natural number, k, such that q=2k; then q must belong to A.
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