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Math Help - Sets-Using De Morgan's Law

  1. #1
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    Sets-Using De Morgan's Law

    Can anyone run through the answer to this for me.
    I'm a bit confused.

    Let X and Y be subsets of some universal set U.
    Use De Morgan's Laws to show that:
    ______
    (X n Y ) n Y is equal to one of the following:

    _
    X n Y
    _
    X u Y

    X

    Y
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  2. #2
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    Hello, mcdonagh521!

    Let X and Y be subsets of some universal set U.

    Use DeMorgan's Laws to show that: . (\overline{X \cap Y}) \cap Y is equal to one of the following:

    . . (a)\;\overline X \cap Y \qquad(b)\;\overline X \cup Y \qquad(c)\;X \qquad (d)\;Y

    We have: . (\overline{X \cap Y}) \cap Y \;=\;(\overline X \cup \overline Y) \cap Y

    . . . . . . . . . . . . . . . . = \;(\overline X \cap Y) \cup (\overline Y \cap Y)

    . . . . . . . . . . . . . . . . = \;(\overline X \cap Y) \cup\; \emptyset

    . . . . . . . . . . . . . . . . = \;\overline X \cap Y . . . answer (a)

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