Sets MCQ test 1

Q1. The cartesian product of two sets P and Q can be written as

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P.Q

PXQ

1.PQ

None of these

Q2. If A = { 1, 3, 5} and B = {2, 3}, then Find: A × B

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[{2, 1},{2, 3},{2, 5},{3, 1},{3, 3},{3, 5}]

[{1, 2},{1, 3},{3, 2},{3, 3},{5, 2},{5, 3}]

6

None of these

Q3. If : (𝒙5,𝒚+1)=(32,∛27) , then : (𝒙,𝒚)=......

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(2,3)

(32,27)

(2,2)

(5,2)

Q4. What will be Cardinality of Cartesian product of a non empty set with a set containing element Φ?
A={1,2,3} and B={Φ}

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0

3

6

9

Q5. If A = {-1, 1, 2}, then n(A x A x A) =

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9

16

27

3

Q6. If A ={3, 5},then A x A x A is......

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{(3, 3), (3, 5), (5, 3), (5, 5)}

{(3, 3, 3), (3, 3, 5), (3, 5, 3), (5, 3, 3), (3, 5, 5), (5, 3, 5), (5, 5, 3), (5, 5, 5) }

{(3, 3, 3), (3, 3, 5), (3, 5, 3), (5, 5, 5)}

{(3, 3, 3), (5, 5, 5)}

Q7. If A = {3, 4} and B = {5, 6} then B x A is.......

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{(5, 3), (5, 4), (6, 3), (6, 4)}

{(3, 5), (3, 6), (4, 5), (4, 6)}

{3, 4, 5, 6}

Φ

Q8.If n(A) = 3, n(B) = 2 and if (x, 4), (y, 5), (z, 4) are three distinct elements of A x B, then

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A = {4, x, y} and B = {5, z}

A = {x, y, z} and B = {4, 5}

A ={y, z, 5} and B = {x, 4}

A = {4, 5} and B = {x, y, z}

Q9. If A × B = {(x, a), (x, b), (y,a), (y, b)} then A =........

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{a,b}

{x,y}

{x,x,y,y}

{x,a}

Q10. If n(A) = 3 and n(B) =4 then find the number of elements in the power set of A × B

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64

24

4096

8

Q11. If two sets A and B have 99 elements in common, then the number of elements common to each of the sets A x B and B x A are

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2^99

99^2

100

18

Q12. If set A has 4 elements and B = {5, 6}, then the number of elements in A x B are .........

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4

8

12

16

Q13. If A = {1, 3, 6}, B = {4, 8} then A x A is ........

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{(1, 3), (1, 6), (3, 1), (3, 6), (6, 1), (6, 3)}

{(1, 4), (1, 8), (3, 4), {(3, 8), (6, 4), (6, 8)}

{(1, 1), (3, 3), (6, 6)}

{(1, 1), (1, 3), (1, 6), (3, 1), (3, 3), (3, 6), (6, 1), (6, 3), (6, 6)}

Q14. If the ordered pairs (x, – 1) and (5, y) belong to the set {(a, b): b = 2a – 3}, find the values of x and y.

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x = 2 and y = 5

x = 1 and y = 7

x = 3 and y = 3

None of these

Q15. Given A = {1, 2, 3}, B = {3, 4}, C = {4, 5, 6}, find (A x B) ∩ (B x C).

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{(3, 4)}

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

(3, 4),(5, 4)

None of these

Q16.If set A = {2, 4, 6}, B = {8, 9} and C = {7, 8}, then find the relation A × (B ∩ C)

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{(2,8), (4,8), (6,8)}

{(2,7), (4,7), (6,7)}

{(2,9), (4,9), (6,9)}

None of these

Q17. For the two non-empty sets A and B, the cartesian product A × B = B × A.

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True

False

Q18. The cartisian product of PXP has 16 elements,among which are found (a,1) and (b,2) then the setP is......

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{a,b}

{a,b,1,2}

{1,2}

None of these

Q19. The Cartesian product of sets A and B is: A x B = {(a,b), a ∈ B and b ∈ A}

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True

False

Q20. If P X Q is an empty set then which of the following is a null set?

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only P

only Q

either P or Q

None of these