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Math Help - this i need guidance on this... please use these rules with a similar example

  1. #1
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    Exclamation this i need guidance on this... please use these rules with a similar example

    use the law of algebra of sets to that <br /> <br />
((X \cup Y) \cap (X \cup Y')) \cap ((X' \cup Y) \cap (X' \cup Y')) \;=\;\emptyset<br />
please specify which rules you use in the derivation....

    the laws i've been given for set operations are.....
    idempotent laws
    associative laws
    commutative laws
    distributive laws
    identity laws
    Involution laws
    involution laws
    complement laws
    de morgans laws
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  2. #2
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    Quote Originally Posted by npm1 View Post
    use the law of algebra of sets to that <br /> <br />
((X \cup Y) \cap (X \cup Y')) \cap ((X' \cup Y) \cap (X' \cup Y')) \;=\;\emptyset<br />
please specify which rules you use in the derivation....

    the laws i've been given for set operations are.....
    idempotent laws
    associative laws
    commutative laws
    distributive laws
    identity laws
    Involution laws
    involution laws
    complement laws
    de morgans laws

    Suppose x\in \left(X\cup Y\right)\cap \left(X\cup Y'\right) and show that it must be that x\in X ...now do the same for the other part of the right side of your expression (which is

    almost the same as the left one but with X' instead of X) , and show that it must be that x\in X' ...deduce finally that the whole thing must be the empty set.

    Tonio
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