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Venn diagram question?

Is A' ^ B' the same as (AUB)' ?

^ means intersect. Why or why not?

3 Answers

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  • 1 decade ago
    Favourite answer

    Yes: De Morgans Law:

    Definition: ~P means not P, so that if P is true then ~P is false.

    ~(P U Q) = ~P ^ ~Q

    Explanation:

    (P U Q) means all the elements that are common to both P and Q, in other words (P union Q) or (P or Q).

    ~(P U Q) means Not (P or Q), in other words every element outside the union of P and Q

    We use De Morgans Law to find the negative of statements

    (P U Q), i.e. we want to know what is ~(P U Q). Read as Not (P or Q).

    It was discovered that this negation is the same as :

    ~P ^ ~Q; read as: not P and not Q

    Referring to a Venn diagram it would be the intersection of all things not P and all things not Q.

  • 1 decade ago

    No. it is not the same.

    Because intersect means "common items of both A and B"

    A' means " not in A but in B"

    B' means " not in B but in A"

    A'^B' means " commons items of both A' and B'"

    (AUB) means "combine all the items of both A and B"

    (AUB)' means " not in (AUB)"

  • 1 decade ago

    i think its De Morgan's law. i cant draw venn diagrams over here. you can find this in wikipedia as well. Also, try this site http://www.classontheweb.com/demo/cbse/classonthew...

    Hope this helps

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