Exercise 4

Do this

1. Which of the following are empty sets? Justify your answer.

(i) Set of integers which lie between 2 and 3.

Empty set. There is no integer between 2 and 3.

(ii) Set of natural numbers that are less than 1.

Empty set.Natuaral numbers are starting from 1.So there is no number less than 1.

(iii) Set of odd numbers that have remainder zero, when divided by 2.

Empty set. Odd numbers gives the remainder 1 when divided with 2.

Try this

1. Which of the following sets are empty sets? Justify your answer.

(i) A = {x : x² = 4 and 3x = 9}.

Empty set. value of x not satisfying both conditions.

(ii) The set of all triangles in a plane having the sum of their three angles less than 180.

Empty set. Sum of angles of a triangle is 180°

2. B = {x : x + 5 = 5} is not an empty set. Why?

Because x is 0 in this equation.

1. State which of the following sets are empty and which are not?

(i) The set of straight lines passing through a point.

Not an Empty set.

(ii) Set of odd natural numbers divisible by 2.

Empty set

(iii) {x : x is a natural number, x < 5 and x > 7}

Empty set

(iv) {x : x is a common point to any two parallel lines}

Empty set

(v) Set of even prime numbers.

Not an empty set

2. State which of the following sets are finite and which are infinite. Give reasons for your answer.

(i) A = {x : x ∈ N and x < 100}

Finite set.Because the elements are countable.

(ii) B = {x : x ∈ N and x < 5}

Finite set.Because the elements are countable.

(iii) C = {1², 2², 3², …..}

Infinite set.The elements are uncountable.

(iv) D = {1, 2, 3, 4}

Finite set.The elements are countable.

(v) {x : x is a day of the week}.

Finite set.The elements are countable.

(vi) The set of months in a year.

Finite set.The elements are countable.

(vii) {1, 2, 3, …, 99, 100}

Finite set.The elements are countable.

(viii) The set of prime numbers less than 99.

Finite set.The elements are countable.

3. State whether each of the following set is finite or infinite.

(i) The set of letters in the English alphabet.

Finite set.The elements are countable.

(ii) The set of lines which are parallel to the X-Axis.

Infinite set

(iii) The set of numbers which are multiplies of 5.

Infinite set

(iv) The set of circles passing through the origin (0, 0).

Infinite set

(v) Tick the set which is infinite

(A) The set of whole numbers < 10

Finite set

(B) The set of prime number < 10

Finite set

(C) The set of integers < 10

Infinite set

(D) The set of factors of 10

Finite set

❮ Sets basics