Are these practice questions for Sets based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 11 - Science Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Sets free?

Yes. Every chapter includes free practice questions for Class 11 - Science students to get you started.

What types of questions are included?

The practice set for Sets mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Sets for full coverage.

How many practice questions are there for Sets?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Sets Class 11 Mathematics Practice Questions with Answers

easy

For any two sets A and B, formulate a proof to show that

A - B = A \cap B'\

.

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easy

If

A = \{1, 2, 3, 4\}

,

B = \{3, 4, 5, 6\}

, and

C = \{5, 6, 7, 8\}

, calculate the set

(A \cup B) \cap (B \cup C)

.

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easy

Recall the name of the law represented by the property:

A \cup (B \cup C) = (A \cup B) \cup C

.

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easy

State the definition of a finite set.

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easy

Define a set.

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easy

Formulate the set

A = \{1, \frac{1}{4}, \frac{1}{9}, \frac{1}{16}, \dots\}

in set-builder form.

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easy

Given the universal set

U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}

and a set

A = \{x : x \text{ is a multiple of 3}\}

. Calculate

A'

.

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easy

Write the set

A = \{x : x \text{ is a prime factor of } 154\}

in roster form.

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easy

List all the subsets of the set

C = \{x, y\}

.

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easy

If

P = \{a, e, i\}

and

Q = \{i, o, u\}

, calculate

P \cup Q

.

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easy

Identify if the following collection is a set or not. Justify your answer: 'The collection of the four most beautiful cities in the world.'

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easy

Let set

A

be the set of letters in the word 'LISTEN' and set

B

be the set of letters in the word 'SILENT'. Analyze if sets

A

and

B

are equal. Justify your answer.

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easy

Evaluate the statement: 'If

A \subset C

and

B \subset C

, then

A \cup B \subset C

'. If it is true, provide a proof. If it is false, provide a counterexample.

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easy

Justify why the collection of 'all difficult problems in this chapter' is not a set, while the collection of 'all questions in Exercise 1.1' is a set.

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medium

Let set

A = \{x \in \mathbf{Z} : x^2 \le 9\}

and set

B = \{x \in \mathbf{R} : x^2 - 4x + 3 = 0\}

. Compare the two sets. Determine if

B \subset A

. Calculate

A - B

and

A \cap B

.

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medium

Let A, B, and C be sets. Evaluate the combined conditions

A \cup B = A \cup C

and

A \cap B = A \cap C

. Formulate a proof to show that these two conditions together imply that

B = C

.

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medium

Let the universal set be

U=\{x: x \in \mathbf{Z} \text{ and } 0 \leq x \leq 10\}

. Let

A=\{x: x \in U \text{ and } x \text{ is a prime number}\}

,

B=\{x: x \in U \text{ and } x \text{ is an even number}\}

, and

C=\{1, 2, 3, 4\}

. Calculate (i)

A' \cap B

and (ii)

(A \cup C) - B

.

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medium

Create a specific example of three non-empty sets A, B, and C such that their pairwise intersections are non-empty, but the intersection of all three is empty.

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medium

Analyze which of the following pairs of sets are disjoint. (i)

A = \{x : x \text{ is a prime number less than } 10\}

and

B = \{x : x \text{ is an even integer and } 0 < x < 10\}

. (ii)

C = \{1, 3, 5, 7\}

and

D = \{2, 4, 6, 8\}

.

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medium

Using the definitions of set operations and elements (i.e., not Venn diagrams), formulate a rigorous proof for De Morgan's Law:

(A \cup B)' = A' \cap B'\

.

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medium

Propose a suitable universal set U for the sets

A = \{x : x \text{ is a prime factor of } 210\}

and

B = \{x : x \text{ is a solution of } x^2 - 9x + 14 = 0\}

. Justify your choice.

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medium

Justify, using properties of sets, that the symmetric difference of two sets A and B, defined as

(A - B) \cup (B - A)

, is equal to

(A \cup B) - (A \cap B)

.

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medium

List the elements of the set

A = \{x : x \text{ is a letter in the word 'MATHEMATICS'}\}

in roster form.

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medium

Explain the difference between the symbols

\in

and

\subset

.

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medium

Let

A = [-3, 5)

and

B = (1, 7]

be two intervals on the real number line. Calculate (i)

A \cap B

and (ii)

A - B

.

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medium

Let

U = \{1, 2, 3, 4, 5, 6, 7\}

,

A = \{2, 3, 5\}

, and

B = \{3, 5, 6\}

. Demonstrate that

(A \cup B)' = A' \cap B'

.

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medium

Given the sets

A = \{x : x \text{ is an integer, } -2 \le x < 3\}

and

B = \{y : y \text{ is a whole number, } y < 4\}

. Calculate

(A - B) \cup (B - A)

.

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medium

Let

X = \{x : x \in \mathbf{N} \text{ and } x \le 5\}

and

Y = \{x : x \text{ is an even natural number less than } 8\}

. Calculate

X \cap Y

.

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medium

A student claims that for any non-empty set A with

n

elements, the number of its proper subsets is

2^n - 2

, arguing that both the empty set

\phi

and the set A itself must be excluded. Critique this reasoning and provide the correct formula.

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medium

Represent the set

B = \{1, 8, 27, 64, 125\}

in set-builder form.

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hard

For any three sets A, B, and C, create a proof to show that

A - (B \cup C) = (A - B) \cap (A - C)

.

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hard

Justify that the following three statements are equivalent for any sets A and B within a universal set U: (i)

A \subset B

(ii)

A \cap B' = \phi

(iii)

A' \cup B = U

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hard

Let

A = \{x, y, z\}

. The power set of A, denoted

P(A)

, is the set of all subsets of A. Analyze the following statements and determine if they are correct: (i)

\{x, y\} \in P(A)

(ii)

\{x\} \subset P(A)

.

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hard

Design a proof to show that for any two sets A and B,

A \cup B = (A - B) \cup (B - A) \cup (A \cap B)

and demonstrate that the three sets on the right-hand side are mutually disjoint.

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hard

For any two sets A and B, formulate a proof to show that if the power set of A is a subset of the power set of B, then A is a subset of B. (i.e.,

P(A) \subset P(B) \Rightarrow A \subset B

)

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hard

Evaluate whether the statement

(A \cup B) \cap A' = B - A

is always true for any sets A and B. Justify your answer using set properties.

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hard

Let the universal set be

U = \{ \text{all single digit natural numbers} \}

. Let

A = \{ x \in U : x \text{ is a perfect square} \}

and

B = \{ x \in U : x \text{ is a factor of 12} \}

. First, calculate

A'

and

B'

. Then, analyze the set

(A \cup B)'

by applying De Morgan's law and verifying it through direct calculation.

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SetsClass 11 Mathematics Practice Questions