math

What is the answer of X' cap Y
What is the answer of Y' U Z'
What is the answer of (X \ Z ) '
What is the answer of ( Y \ Z ) ' U X '
X={10 ,20 ,30 ,40 ,50}
Y={30 ,50, 60, 90, 100}
Z={40, 50, 60, 70, 80}
U={200, 300}

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  1. When you deal with complements, the first question to ask is
    do we know the universal set E?

    Here we assume E=Z (integers)

    X'∩Y = Y\X = {10,20,40,60,90,100}
    Y'&cup'Z'= YΔZ= {30,40,70,80,90,100}
    (X\Z)'={10,20,30}' depending what E equals
    (Y\Z)'∩X'
    =((Y\Z)∪X)'
    =({30,90,100}∪{10,20,30,40,50})'
    ={10,20,30,40,50,90,100}'
    depending on what E is.

    (note U cannot be the universal set because it does not contain any of the other members).

    Note:
    you can type
    ∩ as & c a p ;
    ∪ as & c u p ;
    (do not enter interstitial spaces)

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  2. *
    Y'∪Z'= YΔZ= {30,40,70,80,90,100}

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  3. Thank you

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