## ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 5 Sets Objective Type Questions

**Mental Maths**

Question 1.

Fill in the blanks:

(i) If x is not a member of the set A, then symbolically we write it as ……..

(ii) Each element of a set is listed once and only ……….. repetitions are removed.

(iii) A set that contains a limited number of different elements is called a ……… set.

(iv) Two finite sets are called equivalent if and only if they have ………. a number of elements.

Solution:

(i) If x is not a member of the set A, then symbolically we write it as x ∉ A.

(ii) Each element of a set is listed once and only once, repetitions are removed.

(iii) A set that contains a limited number of different elements ¡s called a finite set.

(iv) Two finite sets are called equivalent if and only if they have equal number of elements.

Question 2.

State whether the following statements are true (T) or false (F):

(i) A collection of books is a set.

(ii) If X = {letters of the word PRINCIPAL}, then the cardinal number of set X is 9.

(iii) If P = {letters of the word AHMEDABAD}, then n(P) = 6.

(iv) If A is any set, then A ⊂ A.

(v) An empty set is a subset of every set.

(vi) If set A = {0}, then n{A} = 0.

(vii) If A and B are two sets such that A ⇔ B, then A = B.

Solution:

(i) A collection of books is a set. (False)

Correct:

A collection of different books is a set.

(ii) If X = {letters of the word PRINCIPAL}, then the cardinal number of set X is 9. (False)

Correct:

n(x) = P, R, I, N, C, A, L = 7 not 9

(iii) If P= {letters of the word AHMEDABAD},

then n(P) = 6. (True)

{A, H, M, E, D, B}

(iv) If A is any set, then A ⊂ A. (True)

(v) An empty set is a subset of every set. (True)

(vi) If set A = {0}, then n{A} = 0. (False)

Correct:

{n(A) = 1}

(vii) If A and B are two sets such that A ⇔ B, then A = B. (False)

Correct:

A = B is A ⇔ B but A ⇔ B is not always A = B

**Multiple Choice Questions**

Choose the correct answer from the given four options (3 to 9):

Question 3.

Which of the following collection forms a set?

(a) Collection of 5 odd prime numbers

(b) Collection of 3 most intelligent students of your class

(c) Collection of 4 vowels of the English alphabet

(d) Collection of first 6 months of a year.

Solution:

Collection of 5 odd prime number, Collection of 4 vowels of English alphabet and collection of first 6 months of a year, all are sets but a collection of 3 most intelligent students of your class is not a set, because intelligence is not well defined. (b)

Question 4.

The tabular form for the statement ‘Days of the week starting with the letter T’ will be

(a) {Days of week starting with letter T}

(b) {Tuesday, Thursday}

(c) {x | x is a day of the week starting with letter T}

(d) none of these

Solution:

Days of the week starting with the letter T in tabular form is {Tuesday, Thursday}. (b)

Question 5.

A set with a limited number of distinct elements is called

(a) a finite set

(b) an infinite set

(c) both finite as well as an infinite set

(d) none of these

Solution:

Set with a limited number of distinct elements is called a finite set. (a)

Question 6.

The symbol ↔ stands for

(a) belongs to

(b) is a subset of

(c) is equivalent to

(d) none of these

Solution:

The symbol ↔ stands for is equivalent to. (c)

Question 7.

The empty set is denoted as

(a) {Φ}

(b) { }

(c) {0}

(d) 0

Solution:

Empty set is denoted as { }. (b)

Question 8.

The cardinal number n(A) = for A = {x : x is an odd prime number less than 20} is

(a) 8

(b) 7

(c) 9

(d) 10

Solution:

The cardinal number n(A) = {x : x is an odd prime number less than 20}

= {3, 5, 7, 11, 13, 17, 19}

n( A) = 7 (b)

Question 9.

If A = {x | x is a positive mutliple of 3 less than 20} and B = {x | x is a prime number less than 20}, then n(A) + n(B) is

(a) 6

(b) 8

(c) 13

(d) 14

Solution:

A = {x | x is a positive mutliple of 3 less than 20}

= {3, 6, 9, 12, 15, 18} ⇒ n(A) = 6

B = {x | x is a prime number less than 20}

= {2, 3, 5, 7, 11, 13, 17, 19} ⇒ n(B) = 8

n(A) + n(B) = 6 + 8 = 14 (d)