Sets Test

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Sets Test - 1

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Weekly Quiz Competition

Question 1
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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.
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.
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
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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, k)

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}
Question 6
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Two sets are equal when they have

A
the same number of members

B
the same members

C
members of the same nature

D
None of these

Solution

Two sets are equal when they have the same members.
Question 7
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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 8
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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

As 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 9
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What information can we get from the number of elements present in 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 union of two sets A and B.
As, union cannot provide us any information about the number of elements in seperate sets.

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Sets Test - 1

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Sets Test - 1

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SHARING IS CARING

Question 1

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

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

It simply means a distinct collection of objects.

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

Question 2

{2, 4, 6}

{2, 4, 6, 8, 10}

{2, 4, 6, 8}

None of these

Solution

Question 3

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

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

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

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

Solution

Question 4

Union of two sets

Intersection of two sets

Difference of two sets

Multiplication of two sets

Solution

Question 5

(a, c, v, b, k)

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

{a, c, v, b, k}

{c}

Solution

Question 6

the same number of members

the same members

members of the same nature

None of these

Solution

Question 7

can be counted as they are finite in number

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

can be counted as they have only finite number of factors

None of these

Solution

Question 8

10

25

35

60

Solution

Question 9

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

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.

None of these

Solution

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