Do this

Some numbers are given below. Decide the numbers to which number sets they belong to and does not belong to and express with correct symbols. i) 1           ii) 0          iii) -4            iv) ⅚     v) 1.3      vi) √2       vii) log 2   viii) 0.03   ix) π         x) √-4

THINK AND DISCUS

Can you write the set of rational numbers in roster form?

You might have concluded by your earlier discussion that it is not possible to write the set of rational numbers by showing list of elements in it. You might have also concluded that all the

rational numbers are written in the form of p/q(q is not belong to 0 and p,q are integers).

When we write a set by defining its elements with a “common property”, we can say that the set is in the “set builder form”. Set builder form should follow some syntax. Let us know it by observing an example.

Suppose A is a set of multiples of 3 less than 20. Then, A={3,6,9,12,15,18} and this is roster form of the set A.When we write its set builder form, it is

A={x : x is a multiple of 3, x < 20} and we
read this as “A is the set of elements x such that x is a multiple of 3 and x is less than 20.

Similarly, we can express the rational numbers set as Q={x : x = p/q , p, q are integers and q¹ 0} In the example,

{2, Ramesh, January}

There are three objects forming a set. But they do not share any common property. So we can’t express it in the set builder form.

Note : (i) In roster form, the order in which the elements are listed is immaterial. Thus,the set of digits in the Ramanujam number is {7, 2, 1, 9}

(ii) While writing the elements of a set in roster form, an element is not repeated. For example, the set of letters forming the word “SCHOOL” is {s, c, h, o, l} and not s, c, h, o, o, l}. Therefore a set contains distinct elements.


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