11th Mathematics NCERT Chapter 1
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– Introduction to Sets: The concept of set is fundamental in mathematics and is used in various branches of the subject. Sets are used to define relations, functions, and are essential in geometry, sequences, and probability【4:0†source】.
– Sets and their Representations: Sets are defined as collections of objects where it can be determined if an object belongs to the set or not. Examples include sets of natural numbers, rivers in India, vowels in English alphabet, among others. Specific sets like N for natural numbers and Z for integers are commonly used in mathematics【4:0†source】.
– Laws of Sets: The chapter covers laws related to sets, such as the law of double complementation and laws of the empty set and universal set. These laws can be verified using Venn diagrams【4:1†source】.
– Set Operations: Various set operations are discussed, including complements, unions, intersections, and differences between sets. Examples and exercises are provided to illustrate these operations【4:1†source】.
– Subsets and Proper Subsets: Concepts of subsets, proper subsets, and singleton sets are explained. Examples and solutions demonstrate the relationships between different sets and how to identify subsets【4:3†source】.
What is a universal set typically denoted by?
Provide an example of a possible universal set in human population studies.
Define the difference of two sets A and B using set notation.
Identify which set is equal to the set of letters in the word 'ALLOY'.
State whether the following example is an example of the null set: 'Set of odd natural numbers divisible by 2'. Justify your answer.
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