Finite and Infinite Sets Worksheet

A few practice questions for the students are given below:

Q1: A= {X:X∈R such that X²-7X+12 = 0}, then A is a finite or an infinite set?

Q2: Let A = {1,2,3,4,5} and B= {4,5,6,7,8}, then A∩B is finite or infinite?

Q3: 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.

Q4: 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?

Q5: Let A ={2,4,6,8,10}, how many subsets does the set A have?

Q6: Check whether the given sets are finite or infinite:

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

Q7: Proof the power set of set B = {3, 5, 7 . . . } is an infinite set.

Q8: Check whether the given sets are finite or infinite:

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

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. In this articles we will discuss about the finite and infinite sets, their properties, solved problems and practice questions.

Finite Sets

A finite set has a finite or countable number of elements. It is a set of natural numbers i.e., positive integers and can be easily counted. It is expressed as P = {1, 2, 3, 4, . . ., n} for natural number n. For example, {5, 6, 7, 8} is a set of countable numbers. An empty set { } is also considered a finite set as it has zero elements i.e., P={ } or n(A) = 0.

Example of Fine Sets

• A set of days in a week: ( Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday )
• The set of natural numbers less than 10: {1, 2, 3, 4, 5, 6, 7, 8, 9}
• The set of vowels in the English alphabet: {a, e, i, o, u}
• The set of planets in the Solar System: {Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}

Infinite Set

An infinite set, as the name suggests, has an infinite or uncountable number of elements. It is a set of all whole numbers including non-negative and negative integers. Infinite sets are also known as uncountable sets. We know that two infinite sets always form an infinite set. It is expressed as P = {0, 1, 2, 3, . . . }, a set of all the whole numbers.

Some examples of Infinite Sets are:

• Set of whole numbers
• Set of integers
• Line segments in a plane etc.