GATE | Sudo GATE 2020 Mock III (24 January 2019) | Question 33

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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