Quiz 1: Set Theory and Relation

Quiz on Sets and Relations

Total Questions: 20 | 1 Mark Each

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1. If A = {1,2,3,4}, then the number of elements in A is:

A) 2
B) 3
C) 4
D) 5

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2. Which of the following represents the empty set?

A) {0}
B) { }
C) {1}
D) {0,1}

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3. If A = {1,2,3} and B = {3,4,5}, then A ∪ B is:

A) {3}
B) {1,2,4,5}
C) {1,2,3,4,5}
D) {1,2,3,3,4,5}

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4. If A = {2,4,6,8} and B = {4,6,10}, then A ∩ B is:

A) {2,8}
B) {4,6}
C) {4,6,10}
D) {2,4,6,8,10}

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5. If A = {1,2,3}, then the number of subsets of A is:

A) 3
B) 6
C) 8
D) 9

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6. If A ⊆ B, then:

A) Every element of B belongs to A
B) Every element of A belongs to B
C) A ∩ B = ∅
D) A = B always

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7. If A = {1,2,3,4} and B = {3,4}, then A − B is:

A) {3,4}
B) {1,2}
C) {1,2,3,4}
D) ∅

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8. If A ∩ B = ∅, then A and B are called:

A) Equal sets
B) Equivalent sets
C) Universal sets
D) Disjoint sets

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9. If A = {a,b}, then the power set P(A) contains:

A) 2 elements
B) 3 elements
C) 4 elements
D) 8 elements

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10. If n(A)=20, n(B)=15, and n(A ∩ B)=5, then n(A ∪ B) is:

A) 25
B) 30
C) 35
D) 40

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11. A relation from a set A to a set B is a subset of:

A) A ∪ B
B) A ∩ B
C) A × B
D) B − A

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12. If A = {1,2} and B = {a,b,c}, then the number of elements in A × B is:

A) 2
B) 3
C) 5
D) 6

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13. If A = {1,2}, then A × A is:

A) {(1,1),(2,2)}
B) {1,2,1,2}
C) {(1,1),(1,2),(2,1),(2,2)}
D) {(1,2),(2,1)}

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14. A relation R on A is reflexive if:

A) (a,b) ∈ R ⇒ (b,a) ∈ R
B) (a,a) ∈ R for every a ∈ A
C) (a,b),(b,c) ∈ R ⇒ (a,c) ∉ R
D) (a,a) ∉ R

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15. A relation R is symmetric if:

A) (a,b) ∈ R ⇒ (b,a) ∈ R
B) (a,a) ∈ R for every a
C) (a,b),(b,c) ∈ R ⇒ (a,c) ∈ R
D) (a,b) ∈ R ⇒ (a,a) ∈ R

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16. A relation R is transitive if:

A) (a,b) ∈ R ⇒ (b,a) ∈ R
B) (a,a) ∈ R
C) (a,b) ∈ R and (b,c) ∈ R ⇒ (a,c) ∈ R
D) (a,b) ∉ R

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17. A relation that is reflexive, symmetric, and transitive is called:

A) Universal relation
B) Identity relation
C) Equivalence relation
D) Empty relation

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18. On A = {1,2,3}, the relation R = {(1,1),(2,2),(3,3)} is called:

A) Empty relation
B) Universal relation
C) Identity relation
D) Inverse relation

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19. If R = {(1,a),(2,b),(3,c)}, then the domain of R is:

A) {a,b,c}
B) {1,2,3}
C) {1,a}
D) {1,2,3,a,b,c}

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20. If R = {(1,2),(2,3),(1,3)}, then the range of R is:

A) {1,2}
B) {1,2,3}
C) {2,3}
D) {1,3}