Question 1.

Which of the following are sets? Justify your answer.

1. List of 10 best singers of the world.
2. List of all students in your school.
3. Collection of all non-even numbers.
4. 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.

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

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

 

Question 11.

Draw the Venn diagram for each of the following:

1. (A∪B∪C)
2. (A∪B)∩C’
3. (A∩B∩C)
4. (A∪B)∩(A∩B∩C)’.

 

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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