Results 1 to 3 of 3

Math Help - formal proof of set

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    13

    formal proof of set

    A and B are subsets of X
    give a formal proof that (A union B)^1 = A^1 intersect B^1

    I know that (A union B)^1 contains the set of elements that are in X that are not in the union of A and B

    and i know that A^1 intersect B^1 contains the set of elements resulting from the intersection of the elements that are in X and not in A or B

    How can i build a formal proof from this?

    Thank you in advance
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,418
    Thanks
    1854
    Quote Originally Posted by murielx View Post
    A and B are subsets of X
    give a formal proof that (A union B)^1 = A^1 intersect B^1

    I know that (A union B)^1 contains the set of elements that are in X that are not in the union of A and B

    and i know that A^1 intersect B^1 contains the set of elements resulting from the intersection of the elements that are in X and not in A or B

    How can i build a formal proof from this?

    Thank you in advance
    What are " A^1" and " B^1". Do you mean A' and B', the complements of A and B?

    To prove "set X = set Y" prove "set X is a subset of set Y" and then prove "set Y is a subset of set X"

    To prove "set X is a subset of set Y" start by saying "if a is a member of X" and use whatever you know about X and Y to conclude "a is a member of Y".

    To prove (A\cup B)'= A'\cap B'
    (By the way \cup is "\cup" and \cap is "\cap".)

    you need to prove that (A\cup B)'\subseteq A'\cap B' and then prove A'\cap B'\subseteq (A\cup B)'.

    To prove the first: If a\in (A\cup B)' then a is NOT in A\cup B. That means that a is NOT in either A or B: a\in A' and a\in B'. From that it follows that a\in A'\cap B' and so a\in (A\cup B)'
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2010
    Posts
    13
    so to prove the second, i can write.

    if a \in A' \cap B' then a is not in A \cap B.
    that means that a is not in A and B.
    a \in A' and a \in B'.
    from that it follows that a \in (A \cup B)' and a \in A' \cap B'

    does the last bit follow because of De morgans law?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Formal proof
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: September 18th 2011, 01:05 PM
  2. Formal Proof
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 30th 2011, 02:12 PM
  3. Formal proof
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: June 14th 2009, 11:19 PM
  4. formal proof
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: April 2nd 2009, 10:17 AM
  5. Formal Proof
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 12th 2008, 03:43 PM

Search Tags


/mathhelpforum @mathhelpforum