InterviewSolution
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InterviewSolution
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The graph is the smallest non-modular lattice N5. A lattice is _______ if and only if it does not have a _______ isomorphic to N5.(a) non-modular, complete lattice(b) moduler, semilattice(c) non-modular, sublattice(d) modular, sublatticeI got this question in exam.This key question is from Graphs in section Graphs of Discrete Mathematics |
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Answer» CORRECT answer is (d) modular, sublattice To elaborate: A lattice (L, ∨, ∧) is modular if for all elements a, B, c of L, the following identity HOLDS->modular identity: (a ∧ c) ∨ (b ∧ c) = [(a ∧ c) ∨ b] ∧ c. This condition is equivalent to the following axiom -> modular law: a ≤ c implies a ∨ (b ∧ c) = (a ∨ b) ∧ c. A lattice is modular if and only if it does not have a sublattice ISOMORPHIC to N5. |
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