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A free semilattice has the _______ property.

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A free semilattice has the _______ property.

(a) intersection

(b) commutative and associative

(c) identity

(d) universal

The question was asked in homework.

I want to ask this question from Graphs topic in division Graphs of Discrete Mathematics

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The correct answer is (d) universal

For explanation I would say: Any set X may be used to generate the free semilattice FX. The free semilattice is defined to consist of all of the finite subsets of X with the semilattice operation given by ordinary set union; the free semilattice has the universal property.

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