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Math Help - please help!!

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    15

    Exclamation please help!!

    Could you please help me solve these questions? Thanks

    1. Use Venn diagrams or membership table to demonstrates that:
    A U (B ∩ C)= (A U C) ∩ (A U C) is a true equation for any sets A, B, and C. If you use Venn diagrams , show the three circles overlapping and include a legend pointing out which set is represented by witch shaded regions.

    2. Find the best conclusion for this Lewis Carroll problem . The "best" conclusion is one which uses all of the given information.
    A. No one who is going to a party ever fails to brush his hair.
    B. No one looks fascinating , if he is untidy.
    C. Opium -eaters have no self-command.
    D.Everyone who has brushed his hair looks fascinating.
    E.No one wears white kid gloves unless he is going to a party.
    F. A person is always untidy if he/she has no self -command.

    Assign letters to the statements , write the premises using logic symbols , write a valid argument which leads to the best conclusion , then write the conclusion in words.

    3. Prove this statement : For all X ε { 2,4,6,8,12,19}, 3x +12 is an even number.

    Please help !!! Thanks
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  2. #2
    Member
    Joined
    Oct 2008
    From
    Singapore
    Posts
    160
    I would use the membership table to solve the 1st problem. Set A, B and C with value 1 and 0 and you will be able to prove whether the 2 equations are logically equivalent or not. And i think it is not. Please correct me if i am wrong learning in the process.

    A B C-B ^ C--A U ( B ^ C )-A U C--(A U C) ^ (A U C)
    0 0 0---0---------0----------0------------0
    0 0 1---0---------0----------1------------1
    0 1 0---0---------0----------0------------0
    0 1 1---1---------1----------1------------1
    1 0 0---0---------1----------1------------1
    1 0 1---0---------1----------1------------1
    1 1 0---0---------1----------1------------1
    1 1 1---1---------1----------1------------1
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