Relations (types, equivalence)

Grade 12 Maths — Relations (types, equivalence): 25 practice questions with instant scoring and explanations.

1. If A = {1, 2, 3} and relation R = {(1,1), (2,2), (3,3)}, then R is:
2. A relation is symmetric if (a,b) ∈ R implies:
3. Which of the following is NOT a property of an equivalence relation?
4. If R is a relation on set {1, 2, 3, 4} where (a,b) ∈ R if a ≤ b, then R is:
5. The relation 'is parallel to' on the set of lines is:
6. If A = {a, b, c} and R = {(a,b), (b,a), (b,c), (c,b)}, then R is:
7. A relation R on ℕ defined as mRn if m divides n. This relation is:
8. For a relation to be an equivalence relation, it must be:
9. The relation 'is congruent to' on the set of triangles is:
10. If R = {(1,1), (1,2), (2,1), (2,2)} on {1, 2}, then R is:
11. Which property is NOT satisfied by the relation 'is equal to' on real numbers?
12. A relation is transitive if (a,b) ∈ R and (b,c) ∈ R implies:
13. The number of equivalence relations on a set with 2 elements is:
14. If A = {1, 2, 3} and R is the universal relation, then R is:
15. A relation that is reflexive and transitive but not symmetric is called:
16. The relation 'is perpendicular to' on lines is:
17. If R = {(a,a), (b,b), (c,c), (a,b), (b,a)} on {a, b, c}, then R is:
18. The number of reflexive relations on a set with n elements is:
19. A relation R is antisymmetric if (a,b) ∈ R and (b,a) ∈ R implies:
20. Which of the following is an equivalence relation?
21. The equivalence class of 2 under the relation 'congruence modulo 3' is:
22. A relation that is reflexive, symmetric, and antisymmetric must satisfy:
23. If R and S are equivalence relations on set A, then R ∩ S is:
24. The relation 'has the same cardinality as' on the set of all finite sets is:
25. If R is reflexive on A, then for all a ∈ A: