Let R be a relation on the set N given by R = {a, b) : a = b – 2, b greater than 6}. Then (a) (2, 4) ∈ R (b) (3,8) ∈ R (c) (6, 8) ∈ R (d) (8,7) ∈ R Watch Solution
Which of the following is not an equivalence relation on Z? (a) aRb ⟺ a + b is an even integer (b) aRb ⟺ a – b is a even integer (c) aRb ⟺ a less than b (d) aRb ⟺ a = b Watch Solution
R is a relation on the set Z of integers and it is given by (x, y) ϵ R ⟺ |x – y| ≤ 1. Then, R is (a) reflexive and transitive (b) reflexive and symmetric (c) symmetric and transitive (d) an equivalence relation Watch Solution
The relation R defined on the set A = {1, 2, 3, 4, 5} by R = {(a,b):|a^2-b^2∣ less than 16} is given by (a) {(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)} (b) {(2, 2), (3, 2), (4, 2), (2, 4)} (c) {(3, 3), (4, 3), (5, 4), (3, 4)} (d) none of these Watch Solution
Let R be the relation over the set of all straight lines in a plane such that L1 R L2⟺L1⊥ L2. Then, R is (a) symmetric (b) reflexive (c) transitive (d) an equivalence relation Watch Solution
If A = {a, b, c}, then the relation R = {(b, c)} on A is (a) reflexive only (b) symmetric only (c) transitive only (d) reflexive and transitive only Watch Solution
Let A = {2, 3, 4, 5, …, 17, 18}. Let ‘≃’ be the equivalence relation on A × A, cartesian product of A with itself, defined by (a, b) ≃ (c, d) if ad = bc. Then, the number of ordered pairs of the equivalence class of (3, 2) is (a) 4 (b) 5 (c) 6 (d) 7 Watch Solution
Let A = {1, 2, 3}. Then, the number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is (a) 1 (b) 2 (c) 3 (d) 4 Watch Solution
The relation ‘R’ in N × N such that (a, b) R (c, d) ⟺ a + d = b + c is (a) reflexive but not symmetric (b) reflexive and transitive but not symmetric (c) an equivalence relation (d) none of these Watch Solution
If A = {1, 2, 3}, B = {1, 4, 5, 9} and R is a relation from A to B defined by ‘x is greater than y’. Then, Range of R is (a) {1, 4, 6, 9} (b) (4,6,9} (c) {1} (d) none of these Watch Solution
A relation R is defined form {2, 3, 4, 5} to {3, 6, 7, 10} by x Ry ⟺ x is relatively prime to y. Then, domain of R is (a) {2,3,5} (b) {3,5} (c) {2, 3, 4} (d) {2, 3, 4, 5} Watch Solution
A relation ϕ from C to R is defined by x ϕ ⟺ |x| = y. Which one is correct ? (a) (2+3i) ϕ 13 (b) 3 ϕ (-3) (c) (1+i) ϕ 2 (d) i ϕ 1 Watch Solution
Let R be a relation on N defined by x + 2y = 8. The domain of R is (a) (2, 4, 8} (b) (2, 4, 6, 8} (c) (2, 4, 6} (d) {1, 2, 3, 4} Watch Solution
R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x – 3. Then, R^{-1} is (a) ((8, 11), (10, 13)} (b) {(11,8), (13, 10)} (c) {(10, 13), (8, 11), (8, 10)} (d) none of these Watch Solution
Let R = {(a, a), (b, b), (c, c), (a, b)} be a relation on set A = {a, b, c}. Then, R is (a) identity relation (b) reflexive (c) symmetric (d) equivalence Watch Solution
Let A = {1, 2, 3} and R = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, R is (a) neither reflexive nor transitive (b) neither symmetric nor transitive (c) transitive (d) none of these Watch Solution
If R is the largest equivalence relation on a set A and S is any relation on A, then A. R ⊂ S B. S ⊂ R C. R = S D. none of these Watch Solution
If R is a relation on the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9} given by x R y ⟺ y = 3x, then R = (a) {(3, 1), (6, 2), (8, 2), (9, 3)} (c) {(3, 1), (2, 6), (3, 9)} (b) {(3, 1), (6, 2), (9, 3)} (d) none of these Watch Solution
If R is a relation on the set A = {1, 2, 3} given by R = (1, 1), (2, 2), (3, 3), then R is (a) reflexive (b) symmetric (c) transitive (d) all the three options Watch Solution
If A = {a, b, c, d}, then a relation R = {(a, b), (b, a), (a, a)} on A is A. symmetric and transitive only B. reflexive and transitive only C. symmetric only D. transitive only Watch Solution
S is a relation over the set R of all real numbers and its is given by (a, b) ϵ S ⟺ ab ≥ 0. Then, S is A. symmetric and transitive only B. reflexive and symmetric only C. antisymmetric relation D. an equivalence relation Watch Solution
If the set Z of all integers, which of the following relation R is not an equivalence relation? A. x R y : if x ≤ y B. x R y : if x = y C. x R y : if x – y is an even integer D. x R y : if x ≡ y (mod 3) Watch Solution
Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then, R is A. reflexive but not symmetric B. reflexive but not transitive C. symmetric and transitive D. neither symmetric nor transitive. Watch Solution
The relation S defined on the set R of all real number by the rule a Sb iff a ≥ b is A. an equivalence relation B. reflexive, transitive but not symmetric C. symmetric, transitive but not reflexive D. neither transitive nor reflexive but symmetric Watch Solution
The maximum number of equivalence relations on the set A = {1, 2, 3} is A. 1 B. 2 C. 3 D. 5 Watch Solution
Let R be a relation on the set N of natural numbers defined by n R m if n divides m. Then, R is A. Reflexive and symmetric B. Transitive and symmetric C. Equivalence D. Reflexive, transitive but Not symmetric Watch Solution
Let L denote the set of all straight lines in a plane. Let a relation R be defined by l R m iff l is perpendicular to m for all l, m ϵ L. Then, R is A. reflexive B. symmetric C. transitive D. none of these Watch Solution
Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as a R b if a is congruent to b for all a, b ϵ T. Then, R is A. reflexive but not symmetric B. transitive but not symmetric C. equivalence D. none of these Watch Solution
Consider a non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then, R is A. symmetric but not transitive B. transitive but not symmetric C. Neither symmetric nor transitive D. both symmetric and transitive Watch Solution
For real numbers x and y, define x R y iff x – y+ √2 is an irrational number. Then the relation R is A. reflexive B. symmetric C. transitive D. none of these Watch Solution
