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Chapter Two

Set and Function

The word ‘set’ is familiar to us, such as dinner set, set of natural numbers, set o f
rational numbers etc. As a modern weapon of mathematics, the use of set is
extensive. The German mathematician Geor ge Cantor (1844 – 1918) first explaine d
his opinion about set. He created a sensation in mathematics by expressing the idea
of infinite set and his conception of set is known as ‘set theory’. In this chapter, the
main objectives are to solve problems through using mathematics and symbols from
the conception of set and to acquire knowledge about function.

At the end of this chapter, the students will be able to :
¾ Explain the conception of set and subset and express them by symbols
¾ Describe the method of expressing set
¾ Explain the infinite set and differentiate between finite and infinite set
¾ Explain and examine the union and the intersection of set
¾ Explain power set and form power set with two or three elements
¾ Explain ordered pair and cartesian product
¾ Prove the easy rules of set by example and Venn Diagram and solve various
problems using the rules of set operation
¾ Explain and form sets and functions
¾ Explain what are domain and range
¾ Determine the domain and range of a function
¾ Draw the graph of the function.

Set

Well defined assembling or collection of objects of real or imaginative world is
called sets, such as, the set of three textbook of Bangla, English and Mathematics, set
of first ten natural odd numbers, set of integers, set of real numbers etc.

Set is generally expressed by the capital letters of english alphabets,
A,B,C,..........X,Y,Z. For example, the set of three numbers 2, 4, 6 is A { 2 , 4 , 6 }

Each object or member of set is called set element. Such as, if B {a,b},a and b
are elements of B. The sign of expressing an element is ''.

?aB and read as a belongs to B

bB and read as b belongs to B

no element c is in the above set B.