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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.

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Quick Information Box

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

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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.

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Important Formulas

Empty Set

$\phi=\{\}$

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Equal Sets

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

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Subset Formula

$A\subset B\iff x\in A\Rightarrow x\in B$

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Universal Set

$U=\text{Universal Set}$

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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.

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(ii) Set of even prime numbers

Solution

2 is an even prime number.

Therefore:

This is NOT a null set.

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(iii)

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

Solution

No natural number can satisfy both conditions simultaneously.

Therefore:

This is a null set.

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(iv)

Set of common points of two parallel lines

Solution

Parallel lines never intersect.

Therefore:

This is a null set.

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Question 2

State whether finite or infinite.

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(i) Set of months in a year

Solution

There are 12 months.

Finite set

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(ii)

{1,2,3,...}

Solution

Natural numbers continue endlessly.

Infinite set

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(iii)

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

Solution

Contains 100 elements.

Finite set

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(iv)

Positive integers greater than 100

Solution

Numbers continue infinitely.

Infinite set

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(v)

Prime numbers less than 99

Solution

Limited number of primes exist below 99.

Finite set

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Question 3

State whether finite or infinite.

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(i)

Set of lines parallel to x-axis

Solution

Infinite lines can be drawn parallel to x-axis.

Infinite set

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(ii)

Set of English alphabets

Solution

There are 26 letters.

Finite set

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(iii)

Set of multiples of 5

Solution

Multiples continue endlessly.

Infinite set

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(iv)

Set of animals living on earth

Solution

Number is countable and limited.

Finite set

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(v)

Set of circles passing through origin

Solution

Infinite circles can pass through origin.

Infinite set

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Question 4

State whether:

A = B

or not.

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(i)

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

Solution

Both contain same elements.

A = B

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(ii)

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

Solution

12 belongs to A but not B.

A ≠ B

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(iii)

A={2,4,6,8,10}

B={x:x is positive even integer and x≤10}

Solution

Both represent same elements.

A = B

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(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

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Question 5

Are the following sets equal?

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(i)

A={2,3}

B={x:x²+5x+6=0}

Solution

Solving:

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

Factorizing:

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

Roots:

x=−2,−3

Therefore:

B={−2,−3}

Hence:

A ≠ B

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(ii)

Letters of FOLLOW and WOLF

Solution

FOLLOW = {F,O,L,W}

WOLF = {W,O,L,F}

Both contain same elements.

Sets are equal.

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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

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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

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Exam Tips

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

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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

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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

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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

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FAQ Section

What is a null set?

A set having no element is called null set.

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What is a finite set?

A set having limited number of elements.

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What is an infinite set?

A set having unlimited elements.

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What are equal sets?

Sets having exactly same elements are called equal sets.

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