Sets Questions and Problem Solving in Mathematics

In mathematics, sets is defined as an organized collection of objects. Sets can be represented in set-builder form or roster form. Sets are usually represented in curly braces denoted by {}, for example, B = {1,2,3,4} is a set. Also, check the set symbols here.

In set theory, you will learn about sets maths set questions, set theory problems and solutions. It was developed to describe the collection of objects. The set theory generally defines the different types of sets, symbols, as well as operations performed.

What are the Elements of a Set?

Let us take an example:

B = {1, 2, 3, 4, 5 }

Since a set is usually represented by any capital letter.  Thus, B is the set, and 1, 2, 3, 4, 5 are the elements of the set or members of the set. The elements that are written in the set can be in any order but these elements cannot be repeated. All the set elements are represented in small letters in the case of alphabets.  Also, we can write it as 1 ∈ B, 2 ∈ B, etc. The cardinal number of the set B is 5. Some commonly used sets are as follows:

• N: Set of all natural numbers

• Z: Set of all integers

• Q: Set of all rational numbers

• R: Set of all real numbers

• Z+: Set of all positive integers

What Does Order of Sets Mean?

The order of a set defines the number of elements in a set . It describes the size of a set. The order of the set is also known as the cardinality. 

The size of a set whether it is is a finite set or an infinite set said to be a set of finite order or infinite order, respectively.

Representation of Sets

The sets are represented in curly braces, {}. For example, {2,3,4} or {a,b,c} or {Bat, Ball, Wickets}. The elements in the sets are depicted in either the Statement form,Set builder form or Roster Form. 

Statement Form

The well-defined descriptions of a member of a set in statement form are written and enclosed in the curly brackets.

For example, a set of numbers that are even less than 15.

In statement form, it can be written as {even numbers less than the number 15}.

Roster Form

In Roster form, all the elements of any given set are listed.

For example, the set of natural numbers less than the number 5.

We know that natural number = 1, 2, 3, 4, 5, 6, 7, 8,……….

We know that Natural Number less than 5 = 1, 2, 3, 4

Therefore, the set is N = { 1, 2, 3, 4 }

Set Builder Form

The general form is, A equals { x : property }

Example: Write the following sets in set builder form: A={2, 4, 6, 8}

Solution:

2 = 2 x 1

4 = 2 x 2

6 = 2 x 3

8 = 2 x 4

So, the set builder form is A = {x: x=2n, n ∈ N and 1  ≤ n ≤ 4}

Also, Venn Diagrams are the best way for visualized representation of sets.

Maths Sets Questions 

Maths Sets questions ( maths sets questions and answers) are given in this article for students to make them understand the concept easily. Practicing these set theory problems will help to go through the concept of sets theory problems. It is an important chapter for Class 11 students, hence we have given the questions based on the NCERT curriculum, with respect to the CBSE syllabus. Let’s discuss maths sets questions.

A brief introduction for each of the sub-topic of sets is also provided.

Here are some important definitions :

Sets: A collection of well-defined objects. It is denoted by Capital Letters.

Example: A = {1,2,3,4,5..}. Set A = collection of all natural numbers.

Roster Form : All elements are written in curly braces { }, separated by commas.

Example: R = {1, 3, 7, 21, 2, 6, 14, 42}.

Set Builder Form: The elements of the set represent a common property known as set builder form.

Example, R = {x : x is a vowel in English alphabet}

First, let us see some questions based on the representation of sets.

Maths Sets Questions 

1. Let A and B be Two Given Finite Sets Such That n(A) Equals 20, n(B) Equals 28, and n(A ∪ B) Equals 36, Find n(A ∩ B).

Solution. Using the formula n(A ∪ B) equals n(A) + n(B) - n(A ∩ B), then n(A ∩ B) equals n(A) + n(B) - n(A ∪ B) 

= 20 + 28 - 36 

= 48 - 36 

= 12