Class 11 Maths · Original EZT practice
Sets (Class 11 Maths Chapter 1): the language the rest of maths is written in
Functions, probability, relations - almost every chapter ahead of you in Class 11 and 12 is written in the language of sets. This chapter builds that language: how to write a set, when one set sits inside another, and the three operations - union, intersection, difference - that combine them. Below: the ideas in plain words, then original EZT practice with worked answers. (Note: this is original practice, not a textbook exercise key.)
10 original worked examples, 10 fresh self-check questions, with explained answers. These are not copied textbook exercises, an official chapter index or a full answer key. No affiliation with NCERT is claimed.
Official sources for topic and edition context, checked 17 October 2026:
1. Writing a set: roster and set-builder
A set is a well-defined collection of distinct objects. Roster form lists the members: V = {a, e, i, o, u}. Set-builder form states the rule: V = {x : x is a vowel of the English alphabet}. Order and repetition do not matter: {1, 2, 2, 3} is the same set as {1, 2, 3}.
2. Types of sets
The empty set {} has no members. A singleton has exactly one. Finite sets have a countable number of members; infinite sets do not, like the set of natural numbers. Two sets are equal when they hold exactly the same members.
3. Subsets and the power set
A is a subset of B when every member of A is also in B. Every set is a subset of itself, and the empty set is a subset of every set. A set with n members has 2^n subsets; the set of all subsets is the power set.
4. Union, intersection, difference
Union A U B means everything in A or B or both. Intersection A n B means only what is in both. Difference A - B means what is in A but not in B. On a Venn diagram, union is the whole shaded region of both circles; intersection is the overlap.
5. Counting with the union formula
For finite sets: n(A U B) = n(A) + n(B) - n(A n B). Subtract the overlap once so it is not counted twice. It turns word problems into one line of arithmetic.
Choose, solve, check, then try a fresh question.
Before calculating, read the method prompt and name the condition that makes it useful. Write your own attempt. Open the steps only when you need them, and use the check to catch a wrong sign, unit or interpretation. Finish with the fresh question before reading its answer.
Write a set in two forms
Choose the method: List the members once, then state the rule.
EZT practice question
Write the set of all even natural numbers below 10 in roster and set-builder form.
Show the worked solution
- The even natural numbers below 10 are 2, 4, 6 and 8.
- Set-builder form states the rule instead of the list.
Answer: Roster: {2, 4, 6, 8}; set-builder: {x : x is an even natural number and x < 10}.
Check: All four listed numbers are even and below 10.
Watch for this: Do not include 10 because the rule says below 10.
Now try it yourself
Write the set of odd natural numbers below 10 in roster form.
Check your answer
{1, 3, 5, 7, 9}.
These are the odd natural numbers below 10.
Use each member once
Choose the method: Ignore repeated letters when writing the roster.
EZT practice question
Write {x : x is a letter of the word SCHOOL} in roster form.
Show the worked solution
- The letters are S, C, H, O, O and L.
- A set keeps distinct members only, so the repeated O appears once.
Answer: {S, C, H, O, L} - the repeated O counts once.
Check: The roster has five distinct letters.
Watch for this: Do not write O twice; repetition does not change a set.
Now try it yourself
Write the set of letters in BALL.
Check your answer
{B, A, L}.
The repeated L appears once.
Classify empty, singleton and infinite sets
Choose the method: Count the members that satisfy each rule.
EZT practice question
Classify: (a) {x : x is an even prime number}, (b) {x : x^2 = 9 and x is an even integer}, (c) the set of points on a line.
Show the worked solution
- Only 2 is an even prime.
- No even integer has square 9; a line has infinitely many points.
Answer: (a) singleton; (b) empty; (c) infinite.
Check: 2 fits the first rule, no number fits the second and infinitely many points fit the third.
Watch for this: Do not call { } a singleton; it has zero members.
Now try it yourself
Classify {x : x is a natural number less than 1}.
Check your answer
The empty set.
No natural number is less than 1.
Check whether sets are equal
Choose the method: Compare members, not order or repetition.
EZT practice question
Are {1, 2, 3} and {3, 2, 1, 2} equal?
Show the worked solution
- The first set contains 1, 2 and 3.
- The second contains the same three members; the repeated 2 changes nothing.
Answer: Yes - order and repetition do not change a set; both are the set of the first three natural numbers.
Check: Every member of each set belongs to the other.
Watch for this: Do not count members before removing repetition.
Now try it yourself
Are {a, b} and {b, a, a} equal?
Check your answer
Yes.
Both contain exactly a and b.
List every subset
Choose the method: Start with the empty set, then singletons, then the full set.
EZT practice question
List all subsets of {1, 2}.
Show the worked solution
- The empty set is a subset.
- The singleton subsets are {1} and {2}; the full set is {1, 2}.
Answer: {}, {1}, {2}, {1, 2} - four subsets, and 4 = 2^2.
Check: A two-member set has 2^2 = 4 subsets.
Watch for this: Do not forget the empty set or the set itself.
Now try it yourself
List all subsets of {a}.
Check your answer
{} and {a}.
A one-member set has 2^1 = 2 subsets.
Use the subset-count rule
Choose the method: Raise 2 to the number of members.
EZT practice question
How many subsets does {a, b, c, d, e} have?
Show the worked solution
- The set has 5 members.
- A set with n members has 2^n subsets.
Answer: 2^5 = 32 subsets.
Check: Each member can independently be in or out, giving 2 choices five times.
Watch for this: Do not multiply 5 by 2; use a power.
Now try it yourself
How many subsets does a 6-member set have?
Check your answer
64.
2^6 = 64.
Test one set against another
Choose the method: Check whether every member of the smaller claim belongs to the larger set.
EZT practice question
Is {2, 4} a subset of {2, 4, 6}? Is {2, 5}?
Show the worked solution
- Both 2 and 4 belong to {2, 4, 6}.
- The member 5 does not.
Answer: {2, 4} is a subset; {2, 5} is not, because 5 is not in the second set.
Check: Every member must belong; one missing member is enough to fail.
Watch for this: Do not test only the common members.
Now try it yourself
Is {1, 3} a subset of {1, 2, 3}?
Check your answer
Yes.
Both 1 and 3 belong to the larger set.
Find union, intersection and difference
Choose the method: Take all members for union, common members for intersection and remaining first-set members for difference.
EZT practice question
A = {2, 4, 6}, B = {4, 6, 8}. Find A U B, A n B and A - B.
Show the worked solution
- Union gathers 2, 4, 6 and 8.
- The common members are 4 and 6; only 2 is in A but not B.
Answer: A U B = {2, 4, 6, 8}; A n B = {4, 6}; A - B = {2}.
Check: The union has four members: 3 + 3 - 2 = 4.
Watch for this: Do not repeat 4 and 6 in the union.
Now try it yourself
For the same sets, find B - A.
Check your answer
{8}.
Only 8 is in B but not A.
Verify the union formula
Choose the method: Count each side independently.
EZT practice question
Verify n(A U B) = n(A) + n(B) - n(A n B) for A = {2, 4, 6}, B = {4, 6, 8}.
Show the worked solution
- n(A) = 3, n(B) = 3 and n(A n B) = 2.
- The formula gives 3 + 3 - 2 = 4.
Answer: n(A) + n(B) - n(A n B) = 3 + 3 - 2 = 4, and A U B = {2, 4, 6, 8} indeed has 4 members.
Check: The two sides agree.
Watch for this: Subtract the overlap once, not twice.
Now try it yourself
If n(A)=5, n(B)=4 and n(A n B)=1, find n(A U B).
Check your answer
8.
5 + 4 - 1 = 8.
Use the union formula in a word problem
Choose the method: Add the two groups, then subtract the students counted twice.
EZT practice question
In a class, 18 students play cricket, 15 play football and 7 play both. How many play at least one of the two games?
Show the worked solution
- Add 18 and 15.
- Subtract the 7 students counted in both groups.
Answer: 18 + 15 - 7 = 26 students.
Check: The 7 students who play both are counted once in the final total.
Watch for this: Do not add 18, 15 and 7; that counts the overlap twice more.
Now try it yourself
20 students like tea, 14 like coffee and 6 like both. How many like at least one?
Check your answer
28.
20 + 14 - 6 = 28.
Try it yourself
Work these on paper before checking any notes. Answers are deliberately not shown here.
- Write the set of prime numbers below 12 in both forms.
- How many subsets does a 6-member set have?
- If A = {1, 3, 5, 7} and B = {1, 2, 3}, find A n B and B - A.
- 20 students like tea, 14 like coffee, 6 like both - how many like at least one?
Know the rule but lose track of the steps?
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Questions about this practice page
- What is a set in maths?
- A well-defined collection of distinct objects - written in roster form by listing members or set-builder form by stating the rule they share.
- What is a subset?
- Set A is a subset of set B when every member of A also belongs to B; an n-member set has exactly 2^n subsets.
- What is the difference between union and intersection?
- Union gathers everything in either set; intersection keeps only what is in both.
- What is the formula for n(A U B)?
- n(A) + n(B) - n(A n B) - the overlap is counted once in each set, so subtract it once.
- Are these the NCERT exercise questions for Sets?
- No. EZT pages are original practice on this chapter - use them to prepare for the textbook exercises, not as a substitute for your book.