Practice question on Set, Relation and Function | part 1

Set, Relation and Function

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Question no. 1

Consider the following statements
1. ∅ ∊ {∅}
2. ∅ ⊆ ∅
which of the statements given above is/ are correct ?

looks_one 1 only

looks_two 2 only

looks_3both 1 and 2

looks_4 neither 1 nor 2

Option 1. 0

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Question no. 32

Coefficients of x in the expansion of

looks_one 9a²

looks_two 10a³

looks_3 10a²

looks_4 10a

Option 1 is correct answer

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Question no. 3

Let A = { x ∊ R | -9 ≤ x < 4 } ; B= { x ∊ R | -13 ≤ x < 5 } ; and C = { x ∊ R | -7 ≤ x < 8 } ; .
then Which one of the following is correct?

looks_one -9 ∊ (A ⋂ B ⋂ C)

looks_two -7 ∊ (A ⋂ B ⋂ C)

looks_3 4 ∊ (A ⋂ B ⋂ C)

looks_4 5 ∊ (A ⋂ B ⋂ C)

Option 4 is correct answer

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Question no. 4

Which one of the following is correct?

looks_oneA ⋃ P(A) = P(A)

looks_twoA ⋃ P(A) = A

looks_3 A - P(A)= A

looks_4 P(A) - {A} = P(A)

Option 2 is correct answer

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Question no. 5

If a set A contains elements , then what is the number of elements in A ✕ P(A)?

looks_one 16

looks_two 32

looks_3 64

looks_4 128

Option 3 is correct answer

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Question no. 6

If A,B,C are three sets such that A ⋃ B = A ⋃ C and A ⋂ B = A ⋂ C , then which one of the following is correct?

looks_one Only A=B

looks_two Only B = C

looks_3 Only A = C

looks_4 A = B = C

Option 2 is correct answer

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Question no. 7

If f : {1,2,3} ➝ {4 ,5} is not a function if it is defined in which one of the following?

looks_one{(2,4) , (3,5) , (1,5)}

looks_two{(1,4) , (2,4) , (3,4)}

looks_3{(1,4) , (2,5) , (3,4)}

looks_4 {(1,4) , (1,5) , (2,4) , (2,5) , (3,4) , (3,5)}

Option 2 is correct answer

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Question no. 8

If A = {1,2,3,4} and R= {(1,1) , (1,3) , (2,2) , (3,1) , (3,4) , (4,3) , (4,4)} is a relation on A ✕ A, then which one of the following is correct ?

looks_one R is reflexive

looks_two R is symmetric and transitive

looks_3 R is transitive but not reflexive

looks_4 R is neither reflexive nor transitive

Option 3 is correct answer

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Question no. 9

What is the number of proper subsets of a given finite set with n elements?

looks_one 2n -1

looks_two 2n -2

looks_3 2ⁿ -1

looks_4 2ⁿ -2

Option 2 is correct answer

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Question no. 10

If A,B and C are three finite sets , then what is {(A ⋃ B)⋂ C }

looks_oneA' ⋃ B' ⋂ C'

looks_twoA' ⋂ B' ⋂ C'

looks_3A' ⋂B' ⋃ C'

looks_4A ⋂ B ⋂ C

Option 1 is correct answer

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Question no. 11

If A and B are subsets of a set X, then what is {A ⋂ (X-B) } equal to ?

looks_one A ⋃ B

looks_two A ⋂ B

looks_3 A

looks_4 B

Option 2 is correct answer

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Question no. 12

Which one of the following is correct ?

looks_oneA ✕ (B - C) = (A-B) ✕ (A-C)

looks_twoA ✕ (B-C)= (A ✕ B) - (A ✕ C)

looks_3A ⋂ (B ⋃ C) = (A ⋂ B) ⋃ C

looks_4A ⋃ (B ⋂ C) = (A⋃ B) ⋂ C

Option 4 is correct answer

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Question no. 13

In the examination out of 100 students , 75 passed in English , 60 passes in Mathematics and 45 passed in both english and Mathematics, what is the number of students passed in exactly one of the two subjects ?

looks_one 45

looks_two 60

looks_3 75

looks_4 90

Option 2 is correct answer

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Question no. 14

Let R = {x | x ∊ N , x is a multiple of 3 and x ≤ 100 } , S = {x | x ∊ N , x is a multiple of 5 and x ≤ 100 } , what is the number of elements in (R ✕ S) ⋂ (S ✕ R) ?

looks_one 36

looks_two 33

looks_3 20

looks_4 6

Option 4 is correct answer

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Question no. 15

If A ={a, b, c } and R = {(a, a), (a,b) ,(b,c) ,(b,b), (c,c), (c,a) } is a binary relation of A , then which one of the following is correct?

looks_oneR is reflexive and symmetric , but not transitive

looks_twoR is reflexive and transitive but not symmetric

looks_3R is reflexive but neither symmetric nor transitive

looks_4 R is reflexive , symmetric and transitive

Option 1 is correct answer

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