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Set Theory and Function

Set : A well defined collection of objects is called a set.

The objects in a set are called its elements or members.

$\dpi{150} \large \mapsto$ If A is a set and x is an element of A, we write, x $\in$ A. If x is not an element of A, we write, x $\notin$ A.

e.g.

(i) If A is the set of vowels in English alphabet, we have

A = { a, e, i, o, u }. Clearly, a $\in$ A, c $\notin$ A, i $\in$ A etc.

(ii) Let B be the set of all integers lying between – 4 and 4, then

B = { – 3, – 2, – 1, 0, 1, 2, 3 }.

(iii) The collection of all intelligent persons of India is not a set, since the term ‘intelligent persons’ is not well defined.

Similarly, ‘Beautiful Ladies’ , ‘ Good Cricketers’, ‘ Honest Students’, etc. do not form sets.