1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Induction of Complementary Sets

  1. Jan 15, 2008 #1
    I'm just wondering how induction can be used to show the following:

    [tex](A_1 \bigcup A_2 \bigcup A_3 \bigcup \cdots \bigcup A_n)^c = A^c_1 \bigcap A^c_2 \bigcap A^c_3 \bigcap \cdots \bigcap A^c_n[/tex]
  2. jcsd
  3. Jan 15, 2008 #2
    What's the base case? Did you try to establish whether a case follows if the previous is true (if the complement of the union of k sets is equivalent to the intersection of their respective complements, does this imply the same for k + 1 sets?).
  4. Jan 15, 2008 #3


    User Avatar
    Science Advisor

    Once you show it for two sets, it is easy. n+1 sets can be considered as 1 set union with n sets. Complement this gives then the complement of 1 set intersected with the complement of the union of n sets.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Induction Complementary Sets Date
I Induction axiom Feb 1, 2018
I Question about mathematical induction Jun 8, 2017
A If the axiom of induction were extended to include imaginary numbers... Aug 11, 2016
I Can you make the induction step by contradiction? Jun 19, 2016
Complementary Logic Nov 6, 2003