Union of Blocks is Set of Points/Corollary

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Corollary to Union of Blocks is Set of Points

Let $\struct {X, \BB}$ be a balanced incomplete block design.


Then the set union of all the subset elements in $\BB$ is precisely $X$.


Proof

By the definition of balanced incomplete block design, $\struct {X, \BB}$ is itself a type of pairwise balanced design.

Thus the corollary follows from Union of Blocks is Set of Points.

$\blacksquare$