Finite Sets and Cardinality

In this Class 11 Mathematics topic from the chapter Sets, students learn how to identify finite sets and determine their cardinality, or the number of distinct elements they contain. The topic introduces standard notation such as n(A), explains how to count elements without repetition, and helps distinguish between an empty set, a finite set, and sets described in different forms. These ideas support clear reasoning when comparing and working with sets.

01If E is the set of months having 28 days in a common year, what kind of set is E?

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Answer and explanation

Correct answer: A. Singleton set

The governing concept is classification by cardinality, meaning by the number of distinct elements in a set. In a common year, February has exactly 28 days, whereas every other month has either 30 or 31 days. Therefore E contains exactly one member: February. Any set with precisely one element is called a singleton set, so option A is correct. It is not empty because February satisfies the condition. It is not infinite because the calendar has a finite number of months. It is not undefined because the phrase “common year” clearly specifies the relevant calendar case. The leap-year situation does not alter the answer because the question explicitly excludes leap years.

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01If E is the set of months having 28 days in a common year, what kind of set is E?

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Finite Sets and Cardinality

Practice questions

01If E is the set of months having 28 days in a common year, what kind of set is E?यदि E = {x : x एक ऐसा महीना है जिसमें सामान्य वर्ष में 28 दिन होते हैं}, तो E कैसा समुच्चय है?

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01If E is the set of months having 28 days in a common year, what kind of set is E?