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**Showcase_22** Suppose S can be separated into $\displaystyle A_1, A_2,.......,A_n$ partitions.

Hence $\displaystyle A_1 \cup A_2 \cup........\cup A_n=S$. Assume that reflexivity, symmetry and transitivity hold.

1). Reflexivity $\displaystyle \Rightarrow A_1 \cap A_i=\phi$ since an element from one subset cannot belong to another subset (property 2 of a partition- the intersections are empty).

This is where I have no idea where to go. Symmetry and transitivity I cannot connect to the definition of a partition.

I was wondering if this is the right idea to follow.