Results 1 to 3 of 3

Math Help - Inverse function of intersection = intersection of inverse functions

  1. #1
    Member oldguynewstudent's Avatar
    Joined
    Oct 2009
    From
    St. Louis Area
    Posts
    241

    Inverse function of intersection = intersection of inverse functions

    From Rosen sixth edition, page 148, section 2.3, 40.b.
    Let f be a function from A to B. Let S and T be subsets of B. Show that

    f inverse(S intesect T) = f inverse (S) intersecting f inverse (T)

    I think I'm starting to get the hang of this but please advise on the correctness!

    f:A->B S subset of B, T subset of B

    Let a be an arbitrary element of f inverse ( S intersecting T) then f(a) is an element of S intersecting T

    so f(a) element of S AND f(a) element of T

    then a element of f inverse (S) AND a element of f inverse (T)

    so a element of (f inverse (S) AND f inverse (T))

    finally a element of f inverse (S) intersecting f inverse (T)

    Since a is an arbitrary element of f inverse (S intersecting T) and
    also of (F inverse (S) intersecting f inverse (T)) this completes the proof.

    Please tell me if and where I've gone wrong.

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Apr 2009
    Posts
    677
    Quote Originally Posted by oldguynewstudent View Post
    From Rosen sixth edition, page 148, section 2.3, 40.b.
    Let f be a function from A to B. Let S and T be subsets of B. Show that

    f inverse(S intesect T) = f inverse (S) intersecting f inverse (T)

    I think I'm starting to get the hang of this but please advise on the correctness!

    f:A->B S subset of B, T subset of B

    Let a be an arbitrary element of f inverse ( S intersecting T) then f(a) is an element of S intersecting T

    so f(a) element of S AND f(a) element of T

    then a element of f inverse (S) AND a element of f inverse (T)

    so a element of (f inverse (S) AND f inverse (T))

    finally a element of f inverse (S) intersecting f inverse (T)

    Since a is an arbitrary element of f inverse (S intersecting T) and
    also of (F inverse (S) intersecting f inverse (T)) this completes the proof.

    Please tell me if and where I've gone wrong.

    Thanks
    You have proved if a belong to f inverse(S intesect T), it belongs to f inverse (S) intersecting f inverse (T)
    Thus f inverse(S intesect T) is a subset of f inverse (S) intersecting f inverse (T)

    What about the other way round. That still needs to be established for equality - correct?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member oldguynewstudent's Avatar
    Joined
    Oct 2009
    From
    St. Louis Area
    Posts
    241
    Quote Originally Posted by aman_cc View Post
    You have proved if a belong to f inverse(S intesect T), it belongs to f inverse (S) intersecting f inverse (T)
    Thus f inverse(S intesect T) is a subset of f inverse (S) intersecting f inverse (T)

    What about the other way round. That still needs to be established for equality - correct?
    Yes, I need to prove the other way for complete proof.

    Thanks, I have a test on Thursday and knowing this is correct will really help!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Proof: Intersection, Inverse Function
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 21st 2011, 12:48 AM
  2. Intersection of inverse functions
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: September 21st 2010, 03:38 PM
  3. Replies: 2
    Last Post: September 8th 2010, 12:27 AM
  4. Intersection of functions --> vector function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 10th 2009, 04:41 AM
  5. Function notations/inverse functions.
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: November 29th 2008, 10:37 AM

Search Tags


/mathhelpforum @mathhelpforum