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Math Help - How to solve these questions?

  1. #1
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    Question How to solve these questions?

    Hello everyone,I would like to ask is there anybody can solve these questions?

    1.)Let A = {a, b}.Does this table define a semigroup and monoid on A?

    * a b
    a a b
    b a b






    2.)Let S = {a,b}. Write the operation table for the semigroup (P(S), ∪).

    I really do not have ideas on how to solve them,that is why I ask here.
    Please explain briefly on how to do the questions,thanks!
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  2. #2
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    Re: How to solve these questions?

    Quote Originally Posted by xenosaga111 View Post
    Hello everyone,I would like to ask is there anybody can solve these questions?

    1.)Let A = {a, b}.Does this table define a semigroup and monoid on A?

    * a b
    a a b
    b a b






    2.)Let S = {a,b}. Write the operation table for the semigroup (P(S), ∪).

    I really do not have ideas on how to solve them,that is why I ask here.
    What are the definitions involved here? How would they be applied here?
    Please show some work.
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  3. #3
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    Re: How to solve these questions?

    There are 16 possible "triple products". For example, 2 of them would be:

    (a*a)*a and a*(a*a)

    For us to have a semigroup, these would have to be equal no matter whether "a" or "b" was in any position.

    From the table, we have:

    a*a = a, so:

    (a*a)*a = (a)*a = a*a = a while:

    a*(a*a) = a*(a) = a*a = a. So for a product involving all a's, we have associativity.

    Now YOU do the other 7 comparisons.
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  4. #4
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    Re: How to solve these questions?

    Are these all the possible combinations for a and b?

    aaa
    aab
    aba
    baa
    abb
    bba
    bab
    bbb
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  5. #5
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    Re: How to solve these questions?

    Actually,what do you mean by definition??Could you please show me some examples??

    Sorry for double post.
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