Relations - Types (reflexive, symmetric, transitive, equivalence)

Grade 12 Maths Higher — Relations - Types (reflexive, symmetric, transitive, equivalence): 25 practice questions with instant scoring and explanations.

1. Let R be a relation on the set of natural numbers defined by R = {(a, b) : a divides b}. Which property does R satisfy?
2. If R = {(x, y) : x² + y² = 1} is a relation on ℝ, which of the following is true?
3. Let R be a relation on integers where aRb if |a - b| ≤ 2. Which property does R NOT have?
4. A relation R on set A is called equivalence if it is:
5. The relation R = {(a, b) : gcd(a, b) = 1} on natural numbers is:
6. If R is a relation where aRb means 'a is parallel to b' (including being the same line), then R is:
7. Let R on ℚ be defined by xRy if x - y ∈ ℤ. How many properties does R have?
8. For a relation to be transitive, if aRb and bRc, then:
9. The relation 'less than or equal to' on real numbers is:
10. If R = {(x, y) : y = |x|} on ℝ, then R is:
11. Let R on positive integers be defined by aRb if a² ≡ b² (mod 5). R is an equivalence relation dividing the set into how many equivalence classes?
12. The relation R = {(a, b) : a + b is even} on integers is:
13. If R is reflexive and transitive but not symmetric, it could be defined as:
14. How many equivalence relations can be defined on a set with 2 elements?
15. If [x] denotes the equivalence class of x under relation R: aRb ⟺ a ≡ b (mod 3) on ℤ, then [5] contains:
16. A relation R on ℤ defined by aRb if |a| = |b| is:
17. For the relation 'is the square root of' on positive reals, which is false?
18. If R = {(a,b) : a² + b² = 25} on ℝ, the number of ordered pairs in R from {3, 4, 5} × {3, 4, 5} is:
19. Let R on ℕ be: aRb iff a and b have the same number of prime factors (with multiplicity). R is:
20. The universal relation on a non-empty set is:
21. If R = {(x, y) : x and y have common factor > 1} on {2, 3, 4, 5, 6}, then R is NOT:
22. How many relations on a set of 2 elements are equivalence relations?
23. For relation R: aRb ⟺ a ≡ b (mod n), the number of equivalence classes is:
24. A relation that is symmetric and transitive must be:
25. The Equivalence Partition Theorem states that an equivalence relation partitions a set into: