Given set A is P a partition of A

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Homework Help Overview

The discussion revolves around determining whether a given collection of subsets, P, is a partition of the set A, where A is defined as {1,2,3,4} and P as {{1,2},{2,3},{3,4}}.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the definition of a partition and its criteria, questioning whether the subsets in P meet these requirements.

Discussion Status

Some participants have provided definitions and criteria for what constitutes a partition, while others are questioning specific aspects of the subsets in P, particularly regarding their intersections and emptiness.

Contextual Notes

There is an emphasis on the formal definition of a partition, and participants are examining whether the subsets in P adhere to these criteria. The original poster's question suggests a potential misunderstanding of the concept.

iHeartof12
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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
 
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What is the definition of a partition? It should make the answer apparent.
 
Last edited:
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
 
Are there any two elements X,Y of P such that X∩Y≠∅ ?
 

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