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Given set A is P a partition of A

  1. Mar 24, 2012 #1
    For the given set A, determine whether P is a partition of A.

    A= {1,2,3,4}, P={{1,2},{2,3},{3,4}}

    Is it correct to say that P is a partition of A?

    Thank you
     
  2. jcsd
  3. Mar 24, 2012 #2
    What is the definition of a partition? It should make the answer apparent.
     
    Last edited: Mar 24, 2012
  4. Mar 24, 2012 #3
    Let A be a nonempty set. P is a partition of A iff P is a set of subsets of A such that

    i. if X [itex]\in[/itex]P, then X ≠∅
    ii. if X [itex]\in[/itex]P and if Y [itex]\in[/itex]P, then X=Y or X[itex]\cap[/itex]Y=∅
    iii. [itex]X\in[/itex]P[itex]\bigcup[/itex]X=A
     
  5. Mar 24, 2012 #4
    Are there any two elements X,Y of P such that X∩Y≠∅ ?
     
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