Sets Test

Result

Sets Test - 2

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Question 1
1 / -0

If A = {a, b, c}, then the number of proper subsets of A is:

A
8

B
10

C
6

D
3

Solution

There are 2ⁿ-2 proper subsets for every set with n elements.

So power set of A = 2³-2 = 6
Question 2
1 / -0

Choose the incorrect statement:

A
Set of all even prime numbers is a subset of set of all natural numbers.

B
If a set has only one element, we call it a singleton set.

C
Φ is not a subset of any set.

D
Every set is a subset of itself.

Solution

Since the empty set Φ has no elements, we say that Φ is a subset of every set.

So the statement in option A is incorrect.
Question 3
1 / -0

A is a set with 6 elements. So, the number of subsets is:

A
64

B
32

C
12

D
24

Solution

If n(A)= m , then the number of subsets of A is 2^m.So, in this case ,

the number of subsets = 2⁶= 64.
Question 4
1 / -0

The set builder form of the set C = {2, 4, 6, 8, 10} is

A
C = {x :x is an even natural number less than 12}

B
C = {x : x is an odd natural number less than 12}

C
C = {x : x is a prime number less than 12}

D
C = {x : x is an even natural number less than 10}

Solution

All the numbers are even natural numbers less than 12.

So option A is correct.
Question 5
1 / -0

Which of the following is a set ?

A
The collection of all interesting novels

B
The collection of all rich persons of Delhi

C
A collection of 10 best writers of India

D
The collection of all the months of a year

Solution

A set is a well defined collection of objects. Since the months of a year are defined, so the collection given in option A is a set.

The sets in options B, C and D have adjectives 'rich', 'interesting' and 'best writers' which are not well-defined. So thoose collections do not form a set.
Question 6
1 / -0

A = {1, 2, 3, 4, 5} and B = {2, 3, 7} So A - B=?

A
{2,3,4}

B
{2,3,7}

C
{1,2,3}

D
{1,4,5}

Solution

A - B = those elements that are in A but not in B = {1, 4, 5}
Question 7
1 / -0

The Roster form of the set A = {x : x is a natural number and a perfect square less than 50} is

A
A = {4, 9, 16, 25}

B
A = {1, 4, 9, 16, 25, 36}

C
A = { 1, 4, 9, 16, 25, 36, 49}

D
A = {10, 11, 15, 20}

Solution

Square of first natural number 1 is 1.

Similarly, 2² = 4, 3² = 9, 4² = 16, 5² = 25, 6² = 36, 7² = 49

8² = 64, which is more than 50.

So, A = {1, 4, 9, 16, 25, 36, 49}

Option C is correct.
Question 8
1 / -0

Identify the null set from the following:

A
The set of points common to two intersecting lines

B
The set of even prime numbers

C
Odd natural numbers divisible by 2

D
The set which contains only zero as its element

Solution

A set which does not contain any element is called the null set.

2 is an even prime number.

The set with '0' as element is not a null set.

Odd natural numbers are not divisible by 2. Hence the given set in option C is a null set.

There is one point common to two intersecting lines. Hence, the set in option D is not a null set.

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Sets Test - 2

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Sets Test - 2

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Question 1

8

10

6

3

Solution

Question 2

Set of all even prime numbers is a subset of set of all natural numbers.

If a set has only one element, we call it a singleton set.

Φ is not a subset of any set.

Every set is a subset of itself.

Solution

Question 3

64

32

12

24

Solution

Question 4

C = {x :x is an even natural number less than 12}

C = {x : x is an odd natural number less than 12}

C = {x : x is a prime number less than 12}

C = {x : x is an even natural number less than 10}

Solution

Question 5

The collection of all interesting novels

The collection of all rich persons of Delhi

A collection of 10 best writers of India

The collection of all the months of a year

Solution

Question 6

{2,3,4}

{2,3,7}

{1,2,3}

{1,4,5}

Solution

Question 7

A = {4, 9, 16, 25}

A = {1, 4, 9, 16, 25, 36}

A = { 1, 4, 9, 16, 25, 36, 49}

A = {10, 11, 15, 20}

Solution

Question 8

The set of points common to two intersecting lines

The set of even prime numbers

Odd natural numbers divisible by 2

The set which contains only zero as its element

Solution

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