Sets Test

Result

Sets Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following statements defines a set in the most appropriate way?

A
It is a method to set an equation and its variables in such a way that they can be solved in an appropriate manner.

B
As the word 'set' is derived from the word 'setting', it is a method to collect distinct objects that are well-defined.

C
It simply means a distinct collection of objects.

D
It is nothing but an assembly or a collection of well-defined distinct elements.

Solution

It is nothing but an assembly or a collection of well-defined distinct elements.
Question 2
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Which of the following is a set of even numbers greater than 1 but less than 10?

A
{2, 4, 6}

B
{2, 4, 6, 8, 10}

C
{2, 4, 6, 8}

D
None of these

Solution

{2, 4, 6, 8} is the set of even numbers greater than 1 but less than 10.
Option (3) is the correct answer.
Question 3
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What do you mean by the union of sets A and B?

A
It is the collection of all those objects which are in set A, but not in set B.

B
It is the set which contains all the elements which are in set B, but not in set A.

C
It is the set which consists of all the elements which belong to set A as well as set B.

D
It is the set which contains all the elements of sets A and B being taken only once.

Solution

As per the definition of union of two sets A and B, union of two sets A and B is the smallest set which contains all the elements of both the sets.
Example:
Let set A = {1, 2, 3, 4, 5}
Set B = {3, 4, 5, 6}
Union of set A and set B = {1, 2, 3, 4, 5, 6}
Here, 3, 4 and 5 are not repeated in union.
Question 4
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Which of the following operations is not a valid operation in set theory?

A
Union of two sets

B
Intersection of two sets

C
Difference of two sets

D
Multiplication of two sets

Solution

Union of two sets, intersection of two sets and difference of two sets are valid operations in set theory, while multiplication is not.
Question 5
1 / -0

Which of the following diagrams correctly represents the union of two sets A and B?

A

B

C

D
None of these

Solution

Union of two sets A and B means the set which contains all the elements of A and B, the common elements taken only once. As option (1) represents set A, option (2) represents A B.
Option (3) is the correct answer.
Question 6
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If set A = {a, c, v} and set B = {b, c, k}, then A B equals ____________.

A
(a, c, v, b)

B
{a, c, v, b, c, k}

C
{a, c, v, b, k}

D
{c}

Solution

According to the definition of union, all the elements in both the sets taken with the common elements are taken only once.
Option (1) is rejected because we represent a finite set within curly brackets { }.
A ∪ B = {a, c, v, b, k}
Hence, option 3 is correct.
Question 7
1 / -0

Two sets are equal when they have

A
same number of members

B
same members

C
members of same nature

D
None of these

Solution

Two sets are equal when they have same members.
Question 8
1 / -0

The set of all odd integers

A
can be counted as they are finite in number

B
can be counted as there is an even number greater than a given odd number

C
can be counted as they have only finite number of factors

D
None of these

Solution

Yes, they can be counted, but the counting will not stop as they are infinite in number.
Question 9
1 / -0

In a group of 50 persons, everyone takes either tea or coffee. If 35 take tea and 25 take coffee, then the number of persons who take both tea and coffee is

A
10

B
25

C
35

D
60

Solution

n(T ∪ C) = n(T) + n(C) - n(T ∩ C)
n(T ∩ C) = n(T) + n(C) - n(T ∪ C)
= 35 + 25 - 50
= 60 - 50
= 10
Question 10
1 / -0

What information can we get from the number of elements present in the union of two sets A and B?

A
It gives us information about the number of elements in set A as well as the number of elements in set B.

B
It gives us information only about the total of number of elements present in set A and the number of elements present in set B.

C
It gives us information about the number of elements in set A plus the number of elements present in set B plus the number of elements present in A as well as B.

D
None of these

Solution

None of the options follows the definition of the union of two sets A and B. Union cannot provide us any information about the number of elements in separate sets.

Question 11

1 / -0

Match the following:

p. Natural numbers (N)	a. {1, 2, 3, …}
q. Whole numbers (W)	b. Integers - negative integers
r. Rational numbers (Q)	c. N W integers Q
s. Real numbers (R)	d. W integers fractions negative fraction

p - b, q - a, r - d, s - c

p - b, q - a, r - c, s - d

p - a, q - b, r - d, s - c

None of these

Solution

The correct matching is: p - a, q - b, r - d, s - c.
p. Natural numbers (N) - a. {1, 2, 3, …}
q. Whole numbers (W) - b. Integers - negative integers
r. Rational numbers (Q) - d. W integers fractions negative fraction
s. Real numbers (R) - c. N W integers Q

Question 12
1 / -0

If set A = {1, 6, 8, 9, 12} and set B = {3, 6, 9, 12}, then A ∩ B equals

A
{3, 6, 9, 12}

B
{6, 9, 12, 6, 9, 12}

C
{6, 9, 12}

D
{1, 6, 8, 9, 12}

Solution

Given set A = {1, 6, 8, 9, 12} and set B = {3, 6, 9, 12}
A ∩ B means the set of all those elements that belong to both A and B.
So,
A ∩ B = {6, 9, 12}
Hence, option (3) is correct.
Question 13
1 / -0

In a group of 15 students, 7 have studied Latin, 8 have studied Greek and 3 have not studied either. How many students have studied both Latin and Greek?

A
0

B
3

C
4

D
5

Solution

Number of students who have studied both Latin and Greek
= 3 + 7 + 8 - 15
= 3
Question 14
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Which of the following sets does not contain any element?

A
Set of all human beings that have put a step on the surface of the moon

B
Set of all human beings who have travelled from New Delhi to New York

C
Set of all those human beings that can live as long as they wish to

D
Set of all the cricketers who have scored a duck in their first innings

Solution

Only option (3) does not contain any element.
Question 15
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Which of the following sets does not contain any element?

A
A set of all those rational numbers whose square is 4

B
A set of all the natural numbers which add up to zero

C
A set of all those rational numbers whose square is zero

D
A set of all those real numbers whose square is 17

E
NA

Solution

There are no natural numbers which add up to zero.
Question 16
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Consider a set A = {3, 15, 4, 7}. If we denote each element of set A as 'n', then which of the following sets represents the elements of the type '2n + 1'?

A
{7, 61, 9, 15}

B
{7, 31, 9, 15}

C
(7, 61, 9, 15)

D
{7, 31, 15, 29}

Solution

Put n = 3, 15, 4 and 7 in (2n + 1).
We get 7, 31, 9 and 15 respectively
So, required set = {7, 31, 9, 15}
Question 17
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If set A = {–3, 2, 3, 7} and we denote each element of set A as 'n', then which of the following sets represents the elements of the type 'n²'?

A
{–9, 4, 49, 9}

B
{4, 9, 49}

C
(4, -9, 49)

D
{9, 4, 9, 49}

Solution

Put n = -3, 2, 3, 7 and find n².So, set representing the elements of the type 'n²' = {4, 9, 49}
Option (4) is rejected as per the definition of set (a set is a collection of distinct objects).
Question 18
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If set A = {16, 4, 121, –9} and we denote each element of set a as 'n', then which of the following sets represents the elements of the type 'n^1/2'_?

A
{4, 2, 11, 3}

B
{4, 2, 11}

C
(4, 2, 11, 3)

D
None of these

Solution

Square root of –9 = 3i
∴ (4, 2, 11, 3i)
Question 19
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Which of the following diagrams correctly represents the intersection of two sets A and B?

A

B

C

D
None of these

Solution

Option (1) represents set A.
Option (2) represents A – B.
Only option (3) represents A B.
Question 20
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If set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and set A = set of all the even numbers in set U, then which of the following diagrams is correct?

A

B

C

D
None of these

Solution

Set A should contain all the even numbers, i.e. 2, 4, 6, 8 and 10.
Rest all numbers should be outside it.
Hence, option (2) is correct.