A = {1,2,3,4,5,6,7,8,9}

R=(A1 x A1) U (A2 x A2) U (A3 x A3) U (A4 x A4)

Proof that R is only Relation that can Partition A like this:

A = {1,2,3} U {4} U {5,6,7} U {8,9}

Note that "U" means Union on Sets.

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