Question:

State whether each of the following set is finite or infinite:
(i) The set of lines which are parallel to the x-axis
(ii) The set of letters in the English alphabet
(iii) The set of numbers which are multiple of 5
(iv) The set of animals living on the earth
(v) The set of circles passing through the origin (0, 0)

Updated On: Oct 22, 2023
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Solution and Explanation

(i) The set of lines which are parallel to the x-axis is an infinite set because lines parallel to the x-axis are infinite
in number.


(ii) The set of letters in the English alphabet is a finite set because it has 26 elements.


(iii) The set of numbers which are multiple of 5 is an infinite set because multiples of 5 are infinite in number.


(iv) The set of animals living on the earth is a finite set because the number of animals living on the earth is finite
(although it is quite a big number).


(v) The set of circles passing through the origin (0, 0) is an infinite set because infinite number of circles can pass
through the origin.

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Concepts Used:

Types of Sets

Sets are of various types depending on their features. They are as follows:

  • Empty Set - It is a set that has no element in it. It is also called a null or void set and is denoted by Φ or {}.
  • Singleton Set - It is a set that contains only one element.
  • Finite Set - A set that has a finite number of elements in it.
  • Infinite Set - A set that has an infinite number of elements in it.
  • Equal Set - Sets in which elements of one set are similar to elements of another set. The sequence of elements can be any but the same elements exist in both sets.
  • Sub Set - Set X will be a subset of Y if all the elements of set X are the same as the element of set Y.
  • Power Set - It is the collection of all subsets of a set X.
  • Universal Set - A basic set that has all the elements of other sets and forms the base for all other sets.
  • Disjoint Set - If there is no common element between two sets, i.e if there is no element of Set A present in Set B and vice versa, then they are called disjoint sets.
  • Overlapping Set - It is the set of two sets that have at least one common element, called overlapping sets.