Practice Problems on Finite and Infinite Sets

Finite and infinite sets are two different parts of "Set theory" in mathematics. When a set has a finite number of elements, it is called a "Finite set" and when a set has an infinite number of elements, it is called an "Infinite set". A finite set is countable, whereas an infinite set is uncountable. The elements in a finite set are natural numbers i.e., non-negative integers. We use dots in a set to represent an infinite set.

Solved Examples

Question 1: Let A = {1, 2, 3, 4} and C = {4, 5, 6, 8} be finite sets. Find the union and intersection of sets A and C.

• The union of two sets A and C can be written as A∪C. It is the set of all the unique elements of both the sets A and C.

Therefore, A∪C = {1, 2, 3, 4, 5, 6, 8}.

• The intersection of the two sets A and C is written as A∩C, is the set of elements which are common in both the sets.

Therefore, A∩C= {4}.

Question 2: Let P = {1, 2, 3, 4, 5, 6} be a finite set. How many subsets does set P have?

• To calculate the subsets of a set, we will use the formula 2ⁿ, where n = the number of elements in the set.

Now, in this question, n = 6

The number of subsets = 2ⁿ = 2⁶ = 64.

Therefore, the set P has 64 subsets including the empty set and the set itself.

Question 3: State whether the given set is finite or infinite.

1) {1,3,5, . . . }

2) {2, 3, 4, 5}

3) { . . . , -3, -2, -1, 0, 1, 2, 3}

4) {10, 20, 30, . . . 200}

1) Infinite

2) Finite

3) Infinite

4) Finite

Question 4: State whether the given set is finite or infinite?

1) {0}

2) {Φ}

3) {X │X∈ N and X>10}

4) { X │X is a prime number}

1) Finite

2) Finite

3) Infinite

4) Infinite

Question5: If Tan θ = 1, then the solution set of the equation is finite or infinite?

Given that tan θ = 1

⇒ tan θ = 1 = tan ?/4

⇒ θ = n? + ?/4 , where n∈Z

⇒ θ = { X : X∈ (n? + ?/4), n∈Z }

The solution of the given question is an infinite set.

Question 6: Consider the following statement:

1) P = {X : X is prime, such that 1> X >10} and A = {2,3,5,7} are equal sets.

2) P = {a,e,i,o,u} and Q = {a,i,o,e,u} are unequal sets.

Which of the following statement is correct?

1) Given, X is prime such that 1> X >10

hence X = 2,3,5,7

P = {2,3,5,7} = A⇒ P=A

Therefore both the sets are equal and the statement is correct.

2) Given, P = {a,e,i,o,u} and Q = {a,i,o,e,u} are unequal sets.

where the order of the elements in a set does not impact the equality of the two sets.

Hence, set P and set Q are equal and the given statement is incorrect.

Question 7:Find out whether the following set is finite or not.

A = {X : X∈N and (X-1) (X-2) = 0}

Given (X-1) (X-2)=0

X= 1,2 then the given set is= (1,2)

As the set has two elements and is countable,

Hence, the set is finite.

Question 8:Identify the set is finite or infinite?

(1, 1/2, 1/4, 1/8, . . . )

The given set is infinite as it has no end point within the set.

Question 9: Find out whether the following site is finite or infinite?

A = {X: X ∈ N and X² = 4}

Given, X² = 4

⇒ X= +2 or -2

⇒ X = 2, -2 but X is a natural number, it can not be negative, hence X = 2

therefore A = (2) which is countable. The set is a finite set.

Related Articles:

• Set Theory
• Set Theory Questions
• Practice Questions on Set Operations

Practice Problems

Question 1: A = {X:X ∈ R such that X² - 7X + 12 = 0}, then A is a finite or an infinite set?

Question 2: Let A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8}, then A∩B is finite or infinite?

Question 3: Let A = {2, 4, 6, 8, 10} and B = {1, 3, 5, 7, 9} be two finite sets. Find the cardinality of the A∪B.

Question 4: let you have two finite sets that have m and n elements, in how many ways you can create a new set by combining elements from both the sets?

Question 5: Let A = {2, 4, 6, 8, 10}, how many subsets does the set A have?

Question 6: Check whether the given sets are finite or infinite:

• Factors of 25 ,
• Multiples of 2,
• Lines segments in a plane

Question 7: Proof the power set of set B = {3, 5, 7 . . . } is an infinite set.

Question 8: Check whether the given sets are finite or infinite:

• P = {2, 4, 6, . . . }
• M = {1, 2, 3, 4, 5}
• X = {a, b, c, . . . }