Sets Test

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Sets Test - 1

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Weekly Quiz Competition

Question 1
1 / -0

Let A = { 1,2,3,4} , B = { 2,3,4,5,6 } , then (A∩B)is equal to :

A
{ 1 }

B
{ 1,2,3 }

C
{ 2,3,4 }

D
{ 5,6 }

Solution

Here A={1,2,3,4} and B={2,3,4,5,6}A∩B={1,2,3,4}∩{2,3,4,5,6}={2,3,4}
Question 2
1 / -0

Let A and B be two sets in the universal set . Then A - B is equal to

A
A−(A∩B)

B
A’ ∩ B

C
A∩ B

D
none of these

Solution

x∈A−B⇒x∈ A but x∉B⇒x∈ A but x∉(A∩B)⇒x∈A−(A∩B)⇒A−B⊆A−(A∩B)similarly

we can show that A−(A∩B)⊆A−B

Hence A−B=A−(A∩B)
Question 3
1 / -0

If A and B are two finite sets such that A ∩ B is not a null set, then n (A ∪ B) is equal to

A
n(A) + n(B)

B
n(A) X n(B)

C
n(A) + n(B) + n(A ∩ B)

D
None of these
Question 4
1 / -0

Let A = { a,b,c } , B = { b,c,d } , C = { a,b,d,e } , then A∩(B∪C) is

A
{ a,b,d,e }

B
{ e }

C
{ b,c,d }

D
{ a,b,c }

Solution

Here A={a,b,c},B={b,c,d }and C={a,b,d,e}B∪C={a,b,c,d,e}A∩(B∪C)={a,b,c}
Question 5
1 / -0

Out of 500 people in a locality, the numbers of people who buy items A, B and C are as given below:
Item A only - 90, item A but not B - 115, items A and C - 40, item A - 130, items B and C - 40, item C - 240, none of the three - 120.
Find the number of people who buy A or B, but not C.

A
105

B
165

C
140

D
None of these
Question 6
1 / -0

Let U = { 1,2,3,4,5,6,7,8,9,10 } , A = { 1,2,5 } , B = { 6,7 }. Then A∩B′ is

A
B

B
A’

C
A

D
B’

Solution

Given U={1,2,3,4,5,6,7,8,9,10},A={1,2,5},B={6,7}B′={1,2,3,4,5,8,9,10}A∩B′={1,2,5}=A
Question 7
1 / -0

The set (A U B UC⁾ ∩ (A ∩ B^c ∩ C^c)^c ∩ C^c is equal to

A
B ∩ C^c

B
A ∩ C

C
A ∩ C^c

D
None of these
Question 8
1 / -0

Let A be the set of all determinants of order 3 with entries 0 or 1 only, B the subset of A consisting of all determinants with value 1 and C the subset consisting of all determinants with value - 1. Which of the following options is correct?

A
n (B) = n (C)

B
A = B U C

C
C = φ

D
None of these
Question 9
1 / -0

Let A and B be two sets such that n(A)=35,n(B)=42 and n(A∩B)=17, find n(A−B)

A
25

B
17

C
18

D
19

Solution

Given that n(A∩B)=17 We have A−B=A−(A∩B) Therefore n(A−B)=n(A)−n(A∩B)=35−17=18
Question 10
1 / -0

In a party, 40 people drank tea, 30 people drank coffee, 25 people drank juice, 15 people drank tea and coffee, 12 people drank juice and tea, 8 people drank coffee and juice and 5 people drank all the three. How many people drank only coffee?

A
15

B
12

C
17

D
Cannot be determined

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Re-Attempt Weekly Quiz Competition

Sets Test - 1

Result

Sets Test - 1

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Rank

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SHARING IS CARING

Question 1

{ 1 }

{ 1,2,3 }

{ 2,3,4 }

{ 5,6 }

Solution

Question 2

A−(A∩B)

A’ ∩ B

A∩ B

none of these

Solution

Question 3

n(A) + n(B)

n(A) X n(B)

n(A) + n(B) + n(A ∩ B)

None of these

Question 4

{ a,b,d,e }

{ e }

{ b,c,d }

{ a,b,c }

Solution

Question 5

105

165

140

None of these

Question 6

B

A’

A

B’

Solution

Question 7

B ∩ Cc

A ∩ C

A ∩ Cc

None of these

Question 8

n (B) = n (C)

A = B U C

C = φ

None of these

Question 9

25

17

18

19

Solution

Question 10

15

12

17

Cannot be determined

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B ∩ C^c

A ∩ C^c