Sets Exercise 1.2 Solutions Class 11 Maths NCERT

Short Intro

In this post, students can find complete step-by-step solutions for Class 11 Maths Chapter 1 Exercise 1.2 – Sets based on the latest NCERT syllabus. This exercise covers null sets, finite and infinite sets, equal sets, subsets, and set properties in a simple and exam-oriented format.

Quick Information Box

Item Details
Board NCERT / CBSE
Class 11
Subject Mathematics
Chapter Sets
Exercise 1.2
Main Topics Null Sets, Finite & Infinite Sets

Concepts Used (Topics Covered)

  • Empty Set (Null Set)
  • Finite Sets
  • Infinite Sets
  • Equal Sets
  • Elements of Sets
  • Set Representation
  • Subsets
  • Universal Set

The chapter explains empty sets, finite and infinite sets, and equal sets.

Important Formulas

Empty Set

ϕ={}\phi=\{\}

Equal Sets

A=B  ⟺  every element of A belongs to B and vice versaA=B\iff \text{every element of }A\text{ belongs to }B\text{ and vice versa}

Subset Formula

A⊂B  ⟺  x∈A⇒x∈BA\subset B\iff x\in A\Rightarrow x\in B

Universal Set

U=Universal SetU=\text{Universal Set}

Questions & Step-by-step Solutions

Question 1

Which of the following are examples of null set?

(i) Set of odd natural numbers divisible by 2

Solution

No odd natural number is divisible by 2.

Therefore:

This is a null set.

(ii) Set of even prime numbers

Solution

2 is an even prime number.

Therefore:

This is NOT a null set.

(iii)

{x:x is natural number,x<5 and x>7}\{x:x\text{ is natural number},x<5\text{ and }x>7\}

Solution

No natural number can satisfy both conditions simultaneously.

Therefore:

This is a null set.

(iv)

Set of common points of two parallel lines

Solution

Parallel lines never intersect.

Therefore:

This is a null set.

Question 2

State whether finite or infinite.

(i) Set of months in a year

Solution

There are 12 months.

Finite set

(ii)

{1,2,3,...}

Solution

Natural numbers continue endlessly.

Infinite set

(iii)

{1,2,3,...,100}

Solution

Contains 100 elements.

Finite set

(iv)

Positive integers greater than 100

Solution

Numbers continue infinitely.

Infinite set

(v)

Prime numbers less than 99

Solution

Limited number of primes exist below 99.

Finite set

Question 3

State whether finite or infinite.

(i)

Set of lines parallel to x-axis

Solution

Infinite lines can be drawn parallel to x-axis.

Infinite set

(ii)

Set of English alphabets

Solution

There are 26 letters.

Finite set

(iii)

Set of multiples of 5

Solution

Multiples continue endlessly.

Infinite set

(iv)

Set of animals living on earth

Solution

Number is countable and limited.

Finite set

(v)

Set of circles passing through origin

Solution

Infinite circles can pass through origin.

Infinite set

Question 4

State whether:

A = B

or not.

(i)

A={a,b,c,d}
B={d,c,b,a}

Solution

Both contain same elements.

A = B

(ii)

A={4,8,12,16}
B={8,4,16,18}

Solution

12 belongs to A but not B.

A ≠ B

(iii)

A={2,4,6,8,10}
B={x:x is positive even integer and x≤10}

Solution

Both represent same elements.

A = B

(iv)

A={x:x is multiple of 10}
B={10,15,20,25,30,...}

Solution

15 and 25 are not multiples of 10.

A ≠ B

Question 5

Are the following sets equal?

(i)

A={2,3}
B={x:x²+5x+6=0}

Solution

Solving:

x2+5x+6=0x^2+5x+6=0

Factorizing:

(x+2)(x+3)=0

Roots:

x=−2,−3

Therefore:

B={−2,−3}

Hence:

A ≠ B

(ii)

Letters of FOLLOW and WOLF

Solution

FOLLOW = {F,O,L,W}

WOLF = {W,O,L,F}

Both contain same elements.

Sets are equal.

Question 6

Select equal sets.

A={2,4,8,12}
B={1,2,3,4}
C={4,8,12,14}
D={3,1,4,2}
E={−1,1}
F={0,a}
G={1,−1}
H={0,1}

Solution

Comparing elements:

B = D

and

E = G

Common Mistakes

  • Repeating elements unnecessarily
  • Confusing empty set with zero
  • Forgetting order does not matter in sets
  • Confusing finite and infinite sets
  • Writing duplicate elements

Exam Tips

  • Memorize important set symbols.
  • Practice roster and set-builder form.
  • Remember that order does not matter in sets.
  • Solve equality questions carefully.

Practice MCQs

MCQ 1

Which is a null set?

A. Even prime numbers
B. Odd numbers divisible by 2
C. Multiples of 5
D. Natural numbers

Answer:

B. Odd numbers divisible by 2

MCQ 2

Which is an infinite set?

A. Months in a year
B. Prime numbers less than 10
C. Natural numbers
D. English alphabets

Answer:

C. Natural numbers

MCQ 3

Equal sets contain:

A. Same number of elements
B. Same order
C. Exactly same elements
D. Same symbols

Answer:

C. Exactly same elements

FAQ Section

What is a null set?

A set having no element is called null set.

What is a finite set?

A set having limited number of elements.

What is an infinite set?

A set having unlimited elements.

What are equal sets?

Sets having exactly same elements are called equal sets.

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