Finite and infinite sets worksheet is much useful to the students who would like to practice problems on set theory.

**State, whether the given set is infinite or finite :**

1) The set of all positive even numbers

2) The set of all whole numbers less than 20

3) The set of all positive integers which are multiples of 3

4) The set of all odd natural numbers less than 15

5) The set of all letters in the word ‘computer’

6) A = { x : x ∈ N, 2 < x ≤ 10 }

7) B = { x : x ∈ Z, (-1/2) < x < 11/2 }

8) C = {x : x is a prime number and a divisor of 6 }

9) D = { x : x = 2ⁿ, n ∈ N and n ≤ 5 }

10) E = { x : x = 2y - 1, y ≤ 5 y ∈ W }

11) F = { x : x is an integer, x**² **≤ 16 }

12) A = {a, e, i, o, u}

13) B = {1, 3, 5, 7, 9, 11}

14) C = {1, 2, 3, 4, 5, ......................}

15) P = {x : x is a letter in the word ‘set theory’}

16) Q = {x : x is a whole number}

17) {x : x is a positive even number}

18) {x : x is a whole number and x < 20}

19) {x : x is a positive integer and multiple of 3}

20) {x : x is an odd natural number and x < 15}

21) {x : x is a letter in the word 'computer'}

22) A = { 3, 4, 5, 6, 7, 8, 9, 10 }

23) B = { 0, 1, 2, 3, 4, 5 }

24) C = { 2, 3 }

25) D = { 2, 4, 8, 16, 32 }

26) E = { -1, 1, 3, 5, 7, 9 }

27) F = { -4, -3, -2, -1, 0, 1, 2, 3, 4 }

28) A is the set of all vowels in the English alphabet

29) B is the set of all natural numbers greater than 1

30) C is the set of all integers less than 0

31) P is the set of all letters in the word ‘set theory’

32) Q is the set of all prime numbers between 10 and 20

1) Infinite

2) Finite

3) Infinite

4) Finite

5) Finite

6) Finite

7) Finite

8) Finite

9) Finite

10) Finite

11) Finite

12) Finite

13) Finite

14) Infinite

15) Finite

16) Infinite

17) Infinite

18) Finite

19) Infinite

20) Finite

21) Finite

22) Finite

23) Finite

24) Finite

25) Finite

26) Finite

27) Finite

28) Finite

29) Infinite

30) Infinite

31) Finite

32) Finite

To understand and solve the problems given in the above worksheet, we have to know the stuff "Finite and infinite sets".

Now, let us look at the stuff "Finite and infinite set".

If the number of elements in a set is zero or finite, then the set is called a finite set.

For example,

(i) Consider the set A of natural numbers between 8 and 9.

There is no natural number between 8 and 9.

So, A = { } and n(A) = 0.

Hence, A is a finite set.

(ii) Consider the set X = { x : x is an integer and -1 ≤ x ≤ 2 }

So, X = { -1, 0, 1, 2 } and n(X) = 4

Hence, X is a finite set.

Note : The cardinal number of a finite set is finite.

A set is said to be an infinite set if the number of elements in the set is not finite.

For example,

Let W = The set of all whole numbers .

That is, W = { 0, 1, 2, 3, ......................}

The set of all whole numbers contain infinite number of elements.

Hence, W is an infinite set.

Note : The cardinal number of an infinite set is not a finite number.

Apart from the stuff "Finite and infinite sets", let us look at the other types of sets in set theory.

After having gone through the stuff given above, we hope that the students would have understood "Finite and infinite sets worksheet".

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