An algebraic structure (L, ∨, ∧), consisting of a set L and two binary operations ∨, and ∧, on L is a lattice if the following axiomatic identities hold for all elements a, b, c of L:
I. Commutative laws II. Associative laws III. Distributive laws IV. Absorption laws
Which of the following conditions are necessary for lattice ?
(A) Only I, II, and III
(B) Only I, II, and IV
(C) Only III and IV
(D) Only II, III, and IV
Answer: (B)
Explanation: A lattice may not be distributive.
Option (B) is correct.
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