Sets Test

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Sets Test - 9

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following is a set?

A
A collection of vowels in English alphabets is a set.

B
The collection of good cricket players of India is a set.

C
The collection of most talented writers of India is a set.

D
The collection of most difficult topics in Mathematics is a set.

Solution

The set is{a,e,i,o,u}
Question 2
1 / -0

Let A = { a ,b ,c } , B = { a, b } , C = { a, b, d } , D = { c , d } and E = { d } . Then which of the following statement is not correct ?

A
C − B = E

B
D ⊇ E

C
B ∪ E = C

D
C − D = E

Solution

C − D = {a,b,d} − {c,d} = {a,b}

But E = {d}

Hence C − D ≠ E
Question 3
1 / -0

If a set A has n elements then the total number of subsets of A is

A
2ⁿ

B
n².

C
2n

D
n

Solution

The total no of subsets=2ⁿ
Question 4
1 / -0

Given the sets A = { 1, 2, 3 } , B = { 3 , 4 } , C = { 4 , 5, 6 } , then A ∪( B ∩ C ) is

A
{1, 2, 3}

B
{ 1, 2 , 3 , 4 }

C
{ 1, 2 ,3 , 4, 5, 6 }

D
{ 3 }

Solution

Given A = {1,2,3},B = {3,4} and C = {4,5,6}

B ∩ C = {4}

A ∪ (B ∩ C) = {1,2,3,4}
Question 5
1 / -0

Sets A and B have 3 and 6 elements respectively . What can be the minimum number of elements in A U B.

A
18

B
6

C
3

D
9

Solution

n(A) = 3

n(B)=6

n(A U B) = n(A) + n(B) -n(A∩B)

for minimum number of elements in A U B

n(A ∩ B)= 3

so n(AUB = 6
Question 6
1 / -0

Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The values of m and n are

A
3 , 3

B
6 , 4

C
7 , 4

D
6 , 3

Solution

Let A and B be two sets having m and n elements respectively.Then,

Number of subsets of A=2^m,Number of subsets of B=2ⁿ

It is given that 2^m-2ⁿ=56

so,2ⁿ(2^m-n-1)=2³(2³-1)

n=3 and m-n=3 ⇒n=3 and m=6
Question 7
1 / -0

The number of proper subsets of the set { 1, 2 , 3 } is :

A
7

B
8

C
5

D
6

Solution

The no of proper subsets=2ⁿ-1=2³-1=7

Here n=no of elements of given set=3

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Re-Attempt Weekly Quiz Competition

Sets Test - 9

Result

Sets Test - 9

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SHARING IS CARING

Question 1

A collection of vowels in English alphabets is a set.

The collection of good cricket players of India is a set.

The collection of most talented writers of India is a set.

The collection of most difficult topics in Mathematics is a set.

Solution

Question 2

C − B = E

D ⊇ E

B ∪ E = C

C − D = E

Solution

Question 3

2n

n2.

2n

n

Solution

Question 4

{1, 2, 3}

{ 1, 2 , 3 , 4 }

{ 1, 2 ,3 , 4, 5, 6 }

{ 3 }

Solution

Question 5

18

6

3

9

Solution

Question 6

3 , 3

6 , 4

7 , 4

6 , 3

Solution

Question 7

7

8

5

6

Solution

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2ⁿ

n².