MTH401

1. Which of the following is a property of an equivalence relation?

a) Reflexive, Symmetric, Transitive b) Reflexive, Antisymmetric, Transitive c) Symmetric, Antisymmetric, Transitive d) Reflexive, Symmetric, Antisymmetric

2. A relation R on a set A is called a partial order if it is:

a) Reflexive, Symmetric, Transitive b) Reflexive, Antisymmetric, Transitive c) Symmetric, Antisymmetric, Transitive d) Reflexive, Symmetric, Antisymmetric

3. A total order is a partial order with the additional property of:

a) Reflexivity b) Symmetry c) Totality d) Antisymmetry

4. Which of the following is true about a lattice?

a) It is a partially ordered set with joins and meets b) It is a totally ordered set c) It is a set with no ordering d) It is a set with only reflexive relations

5. A sublattice of a lattice L is a subset of L that is:

a) Closed under joins and meets b) Closed under joins only c) Closed under meets only d) Not closed under any operation

6. A Hasse diagram is used to represent:

a) Equivalence relations b) Partial orders c) Total orders d) Symmetric relations

7. In a Hasse diagram, an element with no elements below it is called:

a) Minimal element b) Maximal element c) Least element d) Greatest element

8. In a Hasse diagram, an element with no elements above it is called:

a) Minimal element b) Maximal element c) Least element d) Greatest element

9. Which of the following is true about a total order?

a) Every pair of elements is comparable b) Some pairs of elements are incomparable c) It is not transitive d) It is not reflexive

10. A lattice is called distributive if:

a) Join distributes over meet b) Meet distributes over join c) Both join and meet distribute over each other d) Neither join nor meet distributes

11. Which of the following is true about a sublattice?

a) It must contain the least and greatest elements of the original lattice b) It must be closed under joins and meets c) It must be a total order d) It must be an equivalence relation

12. In a Hasse diagram, the least element is:

a) The element at the top b) The element at the bottom c) Any minimal element d) Any maximal element

13. Which of the following is true about a partial order?

a) Every pair of elements is comparable b) Some pairs of elements are incomparable c) It is not transitive d) It is not reflexive

14. A lattice is called bounded if:

a) It has a least and greatest element b) It is distributive c) It is a total order d) It is not reflexive

15. In a Hasse diagram, the greatest element is:

a) The element at the top b) The element at the bottom c) Any minimal element d) Any maximal element

Relations and Lattices

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