Tiêu đề RELATIONS & FUNCTIONS- 2.pdf ✅

6. Let R be a relation on the set N be defined by NCERT Page-3/N-2 {(x, y) ∣ x, y ∈ N, 2x + y = 41}. Then, R is (a) Reflexive (b) Symmetric (c) Transitive (d) None of these 7. Let S be the set of all real numbers. Then, the relation R = {(a, b): 1 + ab > 0} on S is (a) Reflexive and symmetric but not transitive NCERT Page -4/N-4 (b) Reflexive and transitive but not symmetric (c) Symmetric, transitive but not reflexive (d) Reflexive, transitive and symmetric 8. Let L denote the set of all straight lines in a plane. Let a relation R be defined by αRβ ⇔ α ⊥ β, α, β ∈ L. Then, R is NCERT Page-3/N-3 (a) Reflexive (b) Symmetric (c) Transitive (d) None of these 9. For real numbers x and y, we write xRy ⇔ x − y + √2 is an irrational number. Then, the relation R is NCERT/ Page- 2/N − 2 (a) Reflexive (b) Symmetric (c) Transitive (d) None of these 10. Let P = {(x, y) ∣ x 2 + y 2 = 1, x, y ∈ R}. Then, P is NCERT/ Page- 2/N − 2 (a) Reflexive (c) Transitive (b) Symmetric (d) Anti-symmetric 11. Let R1 and R2 be two relations defined on R by a R1b ⇔ ab ≥ 0 and aR2b ⇔ a ≥ b, then NCERT Page N-2 (a) R1 is an equivalence relation but not R2 (b) R2 is an equivalence relation but not R1 (c) both R1 and R2 are equivalence relations (d) neither R1 nor R2 is an equivalence relation 12. For α ∈ N, consider a relation R on N given by R = {(x, y): 3x + αy is a multiple of 7}. The relation R is an equivalence relation if and only if : NCERT Page N − 4 (a) α = 14 (b) α is a multiple of 4 (c) 4 is the remainder when α is divided by 10 (d) 4 is the remainder when α is divided by 7 13. Let R = {(3,3)(5,5), (9,9), (12,12), (5,12), (3,9), (3,12), (3,5)} be a relation on the set A = {3,5,9,12}. Then, R is: NCERT Page-3/N-7 (a) reflexive, symmetric but not transitive. (b) symmetric, transitive but not reflexive. (c) an equivalence relation.