Which of the partially ordered sets are lattices, Mathematics

Which of the partially ordered sets in figures (i), (ii) and (iii) are lattices? Justify your answer.

 

407_Which of the partially ordered sets are lattices.png

Ans: suppose (L, ≤) be a poset. If each subset {x, y} consisting of any two elements of L, has a glb (Infimum) and a lub (Supremum), after that the poset (L, ≤) is known as a lattice. The poset in (i) is a lattice as for each pair of elements in it, there a glb and lub in the poset. Likewise poset in (ii) is as well a lattice. Poset of (iii) is as well a lattice.

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