Home »
MCQs »
Discrete Mathematics MCQs
Discrete Mathematics | Lattices MCQs
Discrete Mathematics | Lattices MCQs: This section contains multiple-choice questions and answers on Lattices in Discrete Mathematics.
Submitted by Anushree Goswami, on November 03, 2022
1. Assume that L is a non-empty set closed only under two binary operations, ____, denoted by ∧ and ∨. It is called a lattice if L has a, b, and c elements, where a, b, and c are the elements in L.
- Meet
- Join
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
Assume that L is a non-empty set closed only under two binary operations, meet and join, denoted by ∧ and ∨. It is called a lattice if L has a, b, and c elements, where a, b, and c are the elements in L.
2. Axioms that lattice L holds are -
- Commutative law
- Associative law
- Absorption law
- All of the above
Answer: D) All of the above
Explanation:
Axioms that lattice L holds are -
- Commutative law
- Associative law
- Absorption law
3. An expression's dual is the expression that can be obtained by _____ ∧ and ∨.
- Mixing
- Interchanging
- Adding
- Removing
Answer: B) Interchanging
Explanation:
An expression's dual is the expression that can be obtained by interchanging ∧ and ∨.
4. The following identities are valid if L is a bounded lattice:
- a ∨ 1 = 1
- a ∧1= a
- a ∨0=a
- All of the above
Answer: D) All of the above
Explanation:
The following identities are valid if L is a bounded lattice:
- a ∨ 1 = 1
- a ∧1= a
- a ∨0=a
5. A non-empty subset L1 of a lattice L is considered. It can be realized that L1 is a ____-lattice of L if it itself is a lattice, i.e., whenever a ∨ b ∈ L1 and a ∧ b ∈ L1 whenever a ∈ L1 and b ∈ L1.
- Super
- Sub
- Side
- None
Answer: B) Sub
Explanation:
A non-empty subset L1 of a lattice L is considered. It can be realized that L1 is a sub-lattice of L if it itself is a lattice, i.e., whenever a ∨ b ∈ L1 and a ∧ b ∈ L1 whenever a ∈ L1 and b ∈ L1.
6. Two lattices L1 and L2 are called isomorphic lattices if there is a ____ from L1 to L2.
- Dijection
- Bijection
- Rejection
- None
Answer: B) Bijection
Explanation:
Two lattices L1 and L2 are called isomorphic lattices if there is a bijection from L1 to L2.
7. If any element a, b, or c of a lattice L satisfies the following distributive properties, it is called a distributive lattice:
- a ∧ (b ∨ c) = (a ∧ b) ∨ (a ∧ c)
- a ∨ (b ∧ c) = (a ∨ b) ∧ (a ∨ c)
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
If any element a, b, or c of a lattice L satisfies the following distributive properties, it is called a distributive lattice:
- a ∧ (b ∨ c) = (a ∧ b) ∨ (a ∧ c)
- a ∨ (b ∧ c) = (a ∨ b) ∧ (a ∨ c)
8. ____ lattices are those that do not satisfy the above properties.
- Non-distributive
- Distributive
- Associative
- Non-associative
Answer: A) Non-distributive
Explanation:
Non-distributive lattices are those that do not satisfy the above properties.
9. An upper bound I and a lower bound o define a bounded lattice L. Assume that a is an element if L. In L, a complementary element x is an element within an if _____.
- a ∨ x = I
- a ∧ x = 0
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
An upper bound I and a lower bound o define a bounded lattice L. Assume that a is an element if L. In L, a complementary element x is an element within an if a ∨ x = I and a ∧ x = 0.
10. _____ are bounded and contain complements for each element.
- Complimented lattices
- Uncomplimented lattices
- Conceptional
- Unconceptional lattices
Answer: A) Complimented lattices
Explanation:
Complimented lattices are bounded and contain complements for each element.
11. (L, b, c) is a modular lattice if a ∨ (b ∧ c) = (a ∨ b) ∧ c whenever ____.
- b ≤ c
- a ≤ b
- a ≤ c
- None
Answer: C) a ≤ c
Explanation:
(L, b, c) is a modular lattice if a ∨ (b ∧ c) = (a ∨ b) ∧ c whenever a ≤ c.
12. (L, ∧,∨) is the ____ of lattices, where L = L1 x L2 where the binary operations (join) and (meet) on L are such that for any (a1,b1) and (a2,b2) in L.
- Direct product
- Indirect product
- Direct sum
- Indirect sum
Answer: A) Direct product
Explanation:
(L, ∧,∨) is the direct product of lattices, where L = L1 x L2 where the binary operations (join) and (meet) on L are such that for any (a1,b1) and (a2,b2) in L.