Daily Practice Problems

Class 11 Maths

Sets

Class 11 Maths

Sets

**Question 1.**

Which of the following are sets? Justify your answer.

- List of 10 best singers of the world.
- List of all students in your school.
- Collection of all non-even numbers.
- List of 15 favourite food of India.

**Question 2.**

Write the set-builder form for A = {1, 16, 81, 256…}.

**Question 3.**

State with reason whether the given statement is true of false.

- c
*⊂*{c, a, t} - ϕ ∈ {1, 2, 3, 10}
- {2, u} ⊄ {a, e, i, o, u, 1, 2}
- {4} ∈ {1, 2, {4,5}, 5}
- {5} ∈ {1, 2, 3, 4, {5}}

**Question 4.**

If A = {0,4,{8}}, write down all the subsets of A and what will be P(A) also use the formula to find the number of subsets.

**Question 5.**

If A ⊂ B and B ⊂ C then A ∪ C =?

**Question 6.**

What will be the universal set of all the words in the English dictionary?

**Question 7.**

If A = {1,2,3,4} and B = {3,4,5,6} then find:

(a) A∪B

(b) A∩B

(c) A-B

(d) B-A.

**Question 8.**

If A = ϕ then find n(P(A)).

**Question 9.**

For any three sets A, B and C. Show that A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C).

**Question 10.**

Write the following as intervals:

- { x : x ∈ R, -8< x ≤19}
- { x : x ∈ R, 0< x <12}
- { x : x ∈ R, 24> x ≥9}
- { x : x ∈ R, -1≤ x ≤1}
- { x : x ∈ R, -9< x ≤-5}.

**Question 11.**

Draw the Venn diagram for each of the following:

**Question 12:**

Two finite sets have m and n elements respectively. The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are:

(a) 7, 6

(b) 5, 1

(c) 6, 3

(d) 8, 7

**Question 13.**

If A = {1, 2, 3, 4}, B = {a, b, c, d}, then what will be the number of elements of P(A∩B)?

**Question 14.**

If A and B are two sets and B′ denotes the complement of B, then B ∩ (A ∪ B)′

is equal to:

(a) A

(b) B

(c) φ

(d) A ∩ B.

**Question 15.**

For A, B and C three sets under the universal set U, if n(U) = 600, n(A) = 250, n(B) = 200 and n(A∩B) = 50. Find n(A’∩B’).

**Question 16.**

If X = {(x, y) : y = e^{-x}; x ∈ W} and Y = {(x, y) : y = e^{x}, x ∈ W}, then what will be the value of (X ∩ Y)?

**Question 17.**

In a class of 80 students, 35 students play chess and 25 students play basketball, and 15 students play both the games. Find the number of students who play neither of them.

**Question 18.**

For any set N = {1, 2, 3, ..., 50},

(i) Write the subset A of N, whose elements are odd numbers.

(ii) Write the subset B of N, whose elements are represented by x + 2;

where x ∈ N.

**Question 19.**

If A and B be the sets defined as follows:

A = { x : x ∈ N , x is divisible by 4 }

B = { y : y ∈ N , y is divisible by 5 }

then A ∩ B = φ is true or false?

**Question 20.**

In a survey, 85 % of Indians like mangoes, whereas 55 % like guavas. What percentage of the Indians like both mangoes and guavas?

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