Results 1 to 8 of 8

Math Help - Need help on a proof

  1. #1
    Junior Member
    Joined
    Feb 2010
    Posts
    33

    Need help on a proof

    Hi everyone, I need help on proving or disproving this:



    Please just show me how to do one of them, and I'd like to try to do the rest on my own. If I don't know then I will post more questions here.
    So far, I've interpreted this question this way:
    i) for all natural numbers n, {there exists natural number j so that m = 5j + 3 and there exists natural number k so that n = 5k + 4, which works for all natural number m} implies that there exists natural number i so that the product mn = 5i + 2
    ii) for all natural numbers m, {there exists natural number i so that m = 5i + 2 and there exists natural number k so that n = 5k + 4, which works for all natural number n} implies that there exists natural number j so that the product mn = 5j + 3
    iii) for all natural numbers m, {there exists natural number i so that m = 5i + 2 and there exists natural number j so that n = 5j + 3, which works for all natural number n} implies that there exists natural number k so that the product mn = 5k + 4

    But this seems so confusing to me, if anyone could point me in the right direction and show me how to do one of those it would be great!
    Thanks in advance!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Selena View Post
    Hi everyone, I need help on proving or disproving this:



    Please just show me how to do one of them, and I'd like to try to do the rest on my own. If I don't know then I will post more questions here.
    So far, I've interpreted this question this way:
    i) for all natural numbers n, {there exists natural number j so that m = 5j + 3 and there exists natural number k so that n = 5k + 4, which works for all natural number m} implies that there exists natural number i so that the product mn = 5i + 2
    ii) for all natural numbers m, {there exists natural number i so that m = 5i + 2 and there exists natural number k so that n = 5k + 4, which works for all natural number n} implies that there exists natural number j so that the product mn = 5j + 3
    iii) for all natural numbers m, {there exists natural number i so that m = 5i + 2 and there exists natural number j so that n = 5j + 3, which works for all natural number n} implies that there exists natural number k so that the product mn = 5k + 4

    But this seems so confusing to me, if anyone could point me in the right direction and show me how to do one of those it would be great!
    Thanks in advance!
    Post your attempt for one of them up here. We will help be better able to help you when we see where your troubles lie.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2010
    Posts
    33
    Yes of course.

    Code:
    Assume n and m are natural numbers:
    	Assume there exists a natural number j and natural number k:
    		Assume:
    		mn = (5j + 3)(5k + 4):
    		   = 25jk + 20j + 15k + 12
    		   = 5(5jk + 4j + 3k) + 12
    		let i = 5jk + 4j + 3k
    		mn = 5i + 12
    		Then mn does not equal 5i + 2
    	Then m = 5j + 3 and n = 5k + 4
    Then V(m) and W(n) together does not imply U(mn)
    That is what I have so far for the first one "i)".
    I'm pretty sure it's wrong though. :x
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Banned
    Joined
    Sep 2009
    Posts
    502
    Quote Originally Posted by Selena View Post
    Hi everyone, I need help on proving or disproving this:



    Please just show me how to do one of them, and I'd like to try to do the rest on my own. If I don't know then I will post more questions here.
    So far, I've interpreted this question this way:
    i) for all natural numbers n, {there exists natural number j so that m = 5j + 3 and there exists natural number k so that n = 5k + 4, which works for all natural number m} implies that there exists natural number i so that the product mn = 5i + 2
    ii) for all natural numbers m, {there exists natural number i so that m = 5i + 2 and there exists natural number k so that n = 5k + 4, which works for all natural number n} implies that there exists natural number j so that the product mn = 5j + 3
    iii) for all natural numbers m, {there exists natural number i so that m = 5i + 2 and there exists natural number j so that n = 5j + 3, which works for all natural number n} implies that there exists natural number k so that the product mn = 5k + 4

    But this seems so confusing to me, if anyone could point me in the right direction and show me how to do one of those it would be great!
    Thanks in advance!
    (i) U(mn) is a set of numbers common to V(m) and W(n) where V(m) and W(n) are sets of numbers such that for all positive integers m and n, m= 5j+2 and n = 5k+4 for some positive integers  j and k
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2009
    Posts
    10
    Hello Selena!

    Quote Originally Posted by Selena View Post
    Yes of course.

    Code:
    Assume n and m are natural numbers:
    	Assume there exists a natural number j and natural number k:
    		Assume:
    		mn = (5j + 3)(5k + 4):
    		   = 25jk + 20j + 15k + 12
    		   = 5(5jk + 4j + 3k) + 12
    		let i = 5jk + 4j + 3k
    		mn = 5i + 12
    		Then mn does not equal 5i + 2
    	Then m = 5j + 3 and n = 5k + 4
    Then V(m) and W(n) together does not imply U(mn)
    That is what I have so far for the first one "i)".
    I'm pretty sure it's wrong though. :x
    Two hints: 12 = 10 + 2 and 10 = 5\cdot 2.

    Best wishes,
    Sebastian
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Feb 2010
    Posts
    33
    Thanks! The 10+2 part was what it was.
    But there's another problem:
    In the "i)", it says "for all n, ...., which works for all m", and the rest are "for all m, ...., which works for all n"; notice that the n and m are switched. Wouldn't that affect the answer?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Nov 2009
    Posts
    10
    Hello Selena!

    Quote Originally Posted by Selena View Post
    But there's another problem:
    In the "i)", it says "for all n, ...., which works for all m", and the rest are "for all m, ...., which works for all n"; notice that the n and m are switched. Wouldn't that affect the answer?
    No, it does not affect the answer. You can use the rule of Universal Elimination and Universal Introduction to prove that the statements which are constituted by switching the n and m are equivalent.

    Best wishes,
    Seppel
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Feb 2010
    Posts
    33
    Quote Originally Posted by Seppel View Post
    Hello Selena!



    No, it does not affect the answer. You can use the rule of Universal Elimination and Universal Introduction to prove that the statements which are constituted by switching the n and m are equivalent.

    Best wishes,
    Seppel
    Oh ok I see, thanks!
    I'm guessing it only affects if it has one or more "exists" in there right?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 15
    Last Post: June 8th 2011, 11:13 AM
  2. Replies: 5
    Last Post: October 19th 2010, 10:50 AM
  3. [SOLVED] direct proof and proof by contradiction
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: February 27th 2010, 10:07 PM
  4. Proof with algebra, and proof by induction (problems)
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: June 8th 2008, 01:20 PM
  5. proof that the proof that .999_ = 1 is not a proof (version)
    Posted in the Advanced Applied Math Forum
    Replies: 4
    Last Post: April 14th 2008, 04:07 PM

Search Tags


/mathhelpforum @mathhelpforum