Question:

Examine whether the following statements are true or false:
(i) {a, b} \(⊄\) {b, c, a}
(ii) {a, e} \(⊂\) {x: x is a vowel in the English alphabet}
(iii) {1, 2, 3} \(⊂\) {1, 3, 5}
(iv) {a} \(⊂ \) {a. b, c}
(v) {a} \(∈\) (a, b, c)
(vi) {x: x is an even natural number less than 6} \(⊂\) {x: x is a natural number which divides 36}

Updated On: Oct 22, 2023
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Solution and Explanation

(i) False. Each element of {a, b} is also an element of {b, c, a}.


(ii) True. a, e are two vowels of the English alphabet.


(iii) False. 2 \(∈\) {1, 2, 3}; however, 2 \(∉\) {1, 3, 5}


(iv) True. Each element of {a} is also an element of {a, b, c}.


(v) False. The elements of {a, b, c} are a, b, c. Therefore, {a} {a, b, c}


(vi) True. {x: x is an even natural number less than 6} = {2, 4} {x: x is a natural number which divides 36} = {1, 2, 3, 4, 6, 9, 12, 18, 36}

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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.