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Math Help - Answer plzzzz

  1. #1
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    Question Answer plzzzz

    1:Set {0}have closure property or not w.r.t both * and+
    2:{0,1} have closure property or not w.r.t both * and+
    please explain your answer
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  2. #2
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    Quote Originally Posted by Peacewanters007 View Post
    1:Set {0}have closure property or not w.r.t both * and+
    2:{0,1} have closure property or not w.r.t both * and+
    please explain your answer
    ****!THANKS 4 SPENDING YOUR PRECIOUS TIME!****
    I'll do number 2, you do number 1.

    In order for a set S to be closed under some operation #, we require that the operation a#b is in S for all a, b belonging to S.

    Define S = \{0, 1 \}

    Then let's do +:
    0 + 0 = 0 \in S

    0 + 1 = 1 \in S

    1 + 0 = 1 \in S

    1 + 1 = 2 \not \in S

    So S is not closed under +.

    Now let's look at *:
    0 * 0 = 0 \in S

    0 * 1 = 0 \in S

    1 * 0 = 0 \in S

    1 + 1 = 1 \in S

    So S is closed under *.

    -Dan
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