important points of Chapter 2: Sets, Functions, and Groups
important points of Chapter 2: Sets, Functions, and Groups Below are the important points of Chapter 2: Sets, Functions, and Groups for 11th Class Mathematics (FBISE syllabus). This chapter covers fundamental concepts of sets, functions, and an introduction to groups, which are critical for understanding higher mathematical structures. 1. Sets A set is a well-defined collection of distinct objects, called elements. Types of Sets : Finite Set : Contains a countable number of elements (e.g., A = \{1, 2, 3\} ). Infinite Set : Contains an uncountable number of elements (e.g., set of all natural numbers). Empty Set : A set with no elements, denoted \emptyset or \{\} . Singleton Set : A set with exactly one element (e.g., \{5\} ). Universal Set : The set containing all elements under consideration, denoted ( U ) . Subset : A \subseteq B if every element of ( A ) is also in ( B ) . Proper Subset : A \subset B if A \subseteq B and A \neq B . Power Set : The set of all subsets of a ...