Given set A is P a partition of A

In summary, for the given set A={1,2,3,4} and partition P={{1,2},{2,3},{3,4}}, the definition of a partition states that P is a set of non-empty subsets of A such that no two subsets have any common elements. Therefore, P is a partition of A.
  • #1
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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  • #2
What is the definition of a partition? It should make the answer apparent.
 
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  • #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
 
  • #4
Are there any two elements X,Y of P such that X∩Y≠∅ ?
 

FAQ: Given set A is P a partition of A

What is a partition?

A partition is a way of dividing a set into non-overlapping subsets, where each element of the original set is included in exactly one of the subsets.

What is the significance of a partition in mathematics?

Partitions are important in mathematics because they allow us to break down a complex problem into smaller, more manageable parts. They also help us to establish relationships and patterns within a set.

How do you determine if a given set is a partition of a larger set?

To determine if a given set is a partition of a larger set, we need to check two things: 1) each element in the larger set must be included in at least one of the subsets, and 2) the subsets must be non-empty and non-overlapping.

Can a set have multiple partitions?

Yes, a set can have multiple partitions. For example, the set of even numbers can be partitioned into subsets of even and odd numbers, or into subsets of prime and composite numbers.

What is the relationship between partitions and equivalence relations?

A partition and an equivalence relation are related in that both involve dividing a set into smaller subsets based on certain criteria. In fact, any equivalence relation on a set will generate a partition of that set, and vice versa.

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