Results 1 to 6 of 6

Math Help - don't understand part of answer to contrapositive question

  1. #1
    Member Jskid's Avatar
    Joined
    Jul 2010
    Posts
    160

    don't understand part of answer to contrapositive question

    Find the contrapositive. If there exists real numbers x and y with x \neq y and x^{2}+x y+y^{2}+x+y=0 then f is not one-to-one

    I got:
    if f is one-to-one then for all real numbers x and y with x=y or x^{2}+x y+y^{2}+x+y \neq 0
    Why is it still = and not \neq?
    Last edited by Jskid; September 8th 2011 at 10:00 PM. Reason: replaced [math] tags with [tex] tags
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28

    Re: don't understand part of answer to contrapositive question

    Hey Jskid

    When thinking about the contrapositive consider this.

    The original statement: if m then n

    Then the contrapositive will be: if not n then not m.

    does this help?

    P.S. to avoid those nasty latex errors use "tex" tags not "math" tags.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member Jskid's Avatar
    Joined
    Jul 2010
    Posts
    160

    Re: don't understand part of answer to contrapositive question

    Quote Originally Posted by pickslides View Post
    Hey Jskid

    When thinking about the contrapositive consider this.

    The original statement: if m then n

    Then the contrapositive will be: if not n then not m.

    does this help?

    P.S. to avoid those nasty latex errors use "tex" tags not "math" tags.
    A little.
    So n is "If there exists real numbers x and y with x \neq y and x^{2}+x y+y^{2}+x+y=0" right?
    Why does the negation change x=y to x \neq y the "and" to "or" but not x^{2}+x y+y^{2}+x+y = 0 to x^{2}+x y+y^{2}+x+y \neq 0?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,537
    Thanks
    778

    Re: don't understand part of answer to contrapositive question

    We have \neg(A\land B)\Leftrightarrow\neg A\lor\neg B\Leftrightarrow A\to\neg B.

    Quote Originally Posted by Jskid View Post
    Find the contrapositive. If there exists real numbers x and y with x \neq y and x^{2}+x y+y^{2}+x+y=0 then f is not one-to-one

    I got:
    if f is one-to-one then for all real numbers x and y with x=y or x^{2}+x y+y^{2}+x+y \neq 0
    Should be: "...then for all real numbers x and y, it is the case that x=y or x^{2}+x y+y^{2}+x+y \neq 0." (The phrase "it is the case that" is inserted just to avoid two mathematical expressions with no words between them.) Alternatively, "...then for all real x and y, if x\ne y, then x^{2}+x y+y^{2}+x+y \neq 0."

    Quote Originally Posted by Jskid View Post
    Why is it still = and not \neq?
    What is "still" = ?. The assumption was x\ne y\land x^{2}+x y+y^{2}+x+y=0; its negation is x=y\lor x^{2}+x y+y^{2}+x+y\ne0.

    Quote Originally Posted by Jskid View Post
    So n is "If there exists real numbers x and y with x \neq y and x^{2}+x y+y^{2}+x+y=0" right?
    Yes, but without the initial "If."

    Quote Originally Posted by Jskid View Post
    Why does the negation change x=y to x \neq y the "and" to "or" but not x^{2}+x y+y^{2}+x+y = 0 to x^{2}+x y+y^{2}+x+y \neq 0?
    The last equation does change to inequation.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member Jskid's Avatar
    Joined
    Jul 2010
    Posts
    160

    Re: don't understand part of answer to contrapositive question

    The answer key has
    If f is one-to-one, then for all real numbers x and y either x=y or x^2+xy+y^2+x+y=0

    is the end a typo? Shouldn't it be \neq 0?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,537
    Thanks
    778

    Re: don't understand part of answer to contrapositive question

    Yes, I think so.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: March 18th 2011, 09:38 AM
  2. Replies: 2
    Last Post: January 22nd 2011, 12:20 PM
  3. cant understand certain part of a solution..
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: August 29th 2009, 09:27 AM
  4. Replies: 1
    Last Post: March 13th 2009, 10:01 PM
  5. Replies: 3
    Last Post: July 20th 2008, 05:24 AM

Search Tags


/mathhelpforum @mathhelpforum