ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 5 Sets Objective Type Questions
Mental Maths
Question 1.
Fill in the blanks:
(i) A collection of ……… objects is called a set.
(ii) If x is a member of the set A, we write it as ………
(iii) The order of listing the elements of a set can be ………
(iv) If one or more elements are repeated, the set remains ………
(v) If X is the set of all letters in the word ‘MATHEMATICS’, then the cardinal number of the set X is ………
Solution:
(i) A collection of well defined objects is called a set.
(ii) If x is a member of the set A, we write it as x e A.
(iii) The order of listing the elements of a set can be changed.
(iv) If one or more elements are repeated, the set remains the same.
(v) If X is the set of all letters in the word ‘MATHEMATICS’, then the cardinal number of the set X is 8.
Question 2.
State whether the following statements are true (T) or false (F). Justify your answer.
(i) A collection of stamps is a set.
(ii) A collection of some fruits is a set.
(iii) A group of boys playing cricket is a set.
(iv) Collection of all students of your class taller than you is a set.
(v) Collection of five rivers of India is a set.
Solution:
(i) A collection of stamps is a set. False
Correct :
It is not a set because it is not known which stamps are included in the collection.
(ii) A collection of some fruits is a set. False
Correct :
It is not a set because it is not known which fruits are included in the collection.
(iii) A group of boys playing cricket is a set. False
Correct :
It is not a set because it is not known which students are included in the group.
(iv) Collection of all students of your class taller than you is a set. True
It is a set because every student of your class can be compared with certainly in relation to your height, so it is very easy to select students of your class who are taller than you i.e. it is well defined collection.
(v) Collection of five rivers of India is a set. False
Correct:
It is not a set because it is not known which five rivers of India are included in the collection.
Multiple Choice Questions
Choose the correct answer from the given four options (3 to 9):
Question 3.
Which of the following collections is a set?
(a) Collection of all tasty fruits
(b) Collection of all good football players of your school
(c) Collection of all months of a year
(d) Collection of 5 most intelligent students of your class.
Solution:
Collection of all months of a year is a set,
If we denote the given set, then A = {January, February, March, April, ……., December} (c)
Question 4.
The tabular form of the statement ‘All months of a year whose names begin with the letters J’ is
(a) {January, June, July}
(b) {months of a year whose names begin with the letter J}
(c) {x | x is a month of a year whose name begins with the letter J}
(d) none of these
Solution:
The given set can be written as in Tabular form :
{January, June, July} (a)
Question 5.
The method of representation used in the set A = {x | x is an even natural number less than 15} is called
(a) Description method
(b) Rule method
(c) Roster method
(d) None of these
Solution:
Rule method (b)
Question 6.
The cardinal number of the empty set is
(a) 2
(b) 1
(c) 0
(d) none of these
Solution:
0 (c)
Question 7.
If S = {x | x is a letter in the word AHMEDABAD}, then the cardinal number of S is
(a) 9
(b) 8
(c) 7
(d) 6
Solution:
S = {Letters Of AHMEDABAD} = {A, H, M, E, D, B} has 6 different elements, so n(S) = 6 (d)
Question 8.
If A = {x : x ϵ N and x is an odd prime number less than 17}, then the cardinal number of A is
(a) 8
(b) 6
(c) 5
(d) none of these
Solution:
Set D = {x : x ϵ N and x is an odd prime number less than 17}
⇒ D = {3, 5, 7, 11, 13}
∴ the cardinal number = 5 (c)
Question 9.
{months of a year whose names begin with the letter F} is
(a) an infinite set
(b) empty set
(c) singleton set
(d) none of these
Solution:
Let A= (months of a year whose name begin with the letter F}
⇒ A = {February}
∴ It is a singleton set. (c)