Chapter 2 Sets, Functions And Groups

Math    Part-I    Chapter-II     "Sets , Functions And Groups

"Following are the key points that should be kept in mind while preparing this chapter in perspective of Entrance test of Universities".

• Understand the real meanings of a 'SET'.

                For example : {1,2,3} is a set but {1,1,2,3,3,1} is not a set by definition.

• Types and Operations on sets.

• Interpretation of Venn Diagram especially Results mentioned at page#39 of Text book.

• Explanation and usage of logic Symbols and related terms used frequently in Aristotelian logic.

• Understand the relation between Logic and Set Theory.

• Function , Types of Functions and Inverse of a function.

• Operations on Residue Classes Modulo Sets.

• Understand Complete Group Theory with all the variations .  For example : If a semi-group with respect to some binary operation also consists Identity of thee operation, It is named as Monoid .

• Real Numbers do not represent a group under Multiplication because Multiplicative Inverse of Zero Doesn't Exist in Real numbers. Moreover  if zero is excluded from 'R' it becomes an Abelian Group.