Given set A is P a partition of A

[iHeartof12]

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

 

[A. Bahat]

What is the definition of a partition? It should make the answer apparent.

 

[iHeartof12]

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 $\in$P, then X ≠∅
ii. if X $\in$P and if Y $\in$P, then X=Y or X$\cap$Y=∅
iii. $X\in$P$\bigcup$X=A

 

[kru_]

Are there any two elements X,Y of P such that X∩Y≠∅ ?