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Prove by induction that size(x) >= 2 rank(x) , where x is the root of a tree in a disjoint-sets forest, and where size(x) returns

Prove by induction that size(x) >= 2rank(x) , where x is the root of a tree in a disjoint-sets forest, and where size(x) returns the number of nodes in the tree rooted by x, if we use both union-by-rank and path-compression when performing the operations of UNION and FIND on this data structure.

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