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Math Help - Questions on set theory

  1. #1
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    Smile Questions on set theory

    Hi

    I need help with the following sets questions

    Let A, B and C be sets. Prove that
    i) A\cap(B\setminus C)=(A\cap B)\setminus(A\cap C)

    Give an example of sets A, B and C for which
    ii) A\cup(B\setminus C)\neq(A\cup B)\setminus(A\cup C)

    I have other proofs of various sets but they involved truth tables. But since these sets involve a subtract set(\), i am not sure on what to do.

    thanks
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  2. #2
    Moo
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    Hello,

    Just recall that A\setminus B=A\cap B^c (the complement of B) and use the usual properties of distribution and associativity of unions and intersections
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  3. #3
    Senior Member Dinkydoe's Avatar
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    For (ii)

    Let A\neq \emptyset and choose B,C arbitrary.
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  4. #4
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by rpatel View Post
    Hi

    I need help with the following sets questions

    Let A, B and C be sets. Prove that
    i) A\cap(B\setminus C)=(A\cap B)\setminus(A\cap C)
    Agree with Moo
    Give an example of sets A, B and C for which
    ii) A\cup(B\setminus C)\neq(A\cup B)\setminus(A\cup C)

    I have other proofs of various sets but they involved truth tables. But since these sets involve a subtract set(\), i am not sure on what to do.

    thanks
    Alternatively, Let C=B=U where U is the universal set. Then, A\cup\left(U\cap U'\right)=A\cup\varnothing=A whereas \left(A\cup U\right)-\left(A\cup U\right)=U-U=\varnothing. I'm sure you can add the extra stipulation to finish this.
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