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!

Homework Help: Simple proof

  1. Sep 7, 2007 #1
    1. The problem statement, all variables and given/known data

    Trying to prove some of the basic laws in set theory, and would like any opinions on 1 of my proofs (eg hints on how can I improve it, is it even a valid proof). Thanks in advance.

    [tex](A \subseteq B \wedge B \subseteq C) \rightarrow (A \subseteq C)[/tex]

    2. Relevant equations

    3. The attempt at a solution

    1) [tex]\forall x \in A, x \in B$[/tex] - definition of a subset
    2) [tex]\forall x \in B, x \in C[/tex] - definition of a subset
    3) [tex]\forall x \in A, x \in C[/tex] - 1, 2
    4) [tex]A \subseteq C[/tex] - 3, definition of a subset
  2. jcsd
  3. Sep 7, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper

    Your logic is correct.

    You could also use proof by contradiction:

    Suppose A [itex]\nsubseteq[/itex] C. Then there must be some a in A that is not in C. Since B [itex]\subseteq[/itex] C, a cannot be in B. This contradicts A [itex]\subseteq[/itex] B.
    Last edited: Sep 7, 2007
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook