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Math Help - Induction proof

  1. #1
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    Induction proof

    Hello Everyone :-)

    1)

    I have to prove with Induction that if Αi⊆U for every positive integer I , where A is an omnium (or group don't remember the right English phrase =/ ) and U is the Whole, i have to prove that :

    2)
    We have a sequence of integers (c) that is for every
    n>= 1 . Prove with induction that for every n>=0

    3)

    Again -.- , i have to prove with induction : for every n > = 1 .

    Well , its not that i am trying to find easy answers on the web without trying at all on my own, but seriously i 've burned my mind already trying to solve them, and nothing happened...

    Thanks in advance for your help :-)
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  2. #2
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    Take 2), for example. First I would recommend writing a table
    Code:
     0 |  1  |  2  |  3  |  4  |
    ---------------------------
    c0 | c1  | c2  | c3  | c4  |
    with several initial values of c_i. Does it fit the general formula? Can you see why, or is it a total surprise? I mean that in order to prove something one has to become comfortable with the concepts of that particular problem and have some intuition why the claim should be true.

    If you did this, you already finished the base case. Now let P(n) be the statement that c_n=3^{2^n}. The induction hypothesis is P(n). What you need to prove is P(n+1) -- be sure to write P(n) and P(n+1) explicitly. If at this point you don't see how to prove P(n+1) from P(n) and the definition of c_{n+1}, post here all of these things and describe your difficulty.
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  3. #3
    Member oldguynewstudent's Avatar
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    DeMorgan's laws

    Quote Originally Posted by primeimplicant View Post
    Hello Everyone :-)

    1)

    I have to prove with Induction that if Αi⊆U for every positive integer I , where A is an omnium (or group don't remember the right English phrase =/ ) and U is the Whole, i have to prove that :

    2)
    We have a sequence of integers (c) that is for every
    n>= 1 . Prove with induction that for every n>=0

    3)

    Again -.- , i have to prove with induction : for every n > = 1 .

    Well , its not that i am trying to find easy answers on the web without trying at all on my own, but seriously i 've burned my mind already trying to solve them, and nothing happened...

    Thanks in advance for your help :-)
    I am in a rush so I don't have time to make this pretty.

    For the basis step the complement of A_1 = the complement of A_1 so the basis step is true.

    Then write out the sequence

    The complement of [ A_1 \cup A_2 \cup ... \cup A_k ] is equal to the intersection of the complements by DeMorgan's law.

    Then just do the same for k+1.

    Hope this helps, I'll check back after my morning classroom observations. Currently taking education classes, observing and helping at an inner city HS.
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