November 1, 2014

10th Maths New Syllabus SETS - Roster Form of Writing Sets

Examples of sets.
1) The Collection of English alphabets.
a, b, c, d, ... x, y, z

2) The collection of Natural numbers
1, 2, 3, ...........

3) The Collection of Prime numbers
2, 3, 5, 7,..............

4) The Collection of the devices of a computer the input device. The central
processing unit, the output device
Examples of collections that are not sets
1) The collection of 5 Tasty sweet dishes.
2) The collection of interesting novels.
3) The collection of easy problems in X Maths text book.
4) The collection of beautiful dresses.
A Set is denoted by upper case letters A, B, C, D,.......... etc.
We have seen the different sets of Numbers in the chapter Real Numbers.

Roster form of writing a set:

When all the elements in the set are listed down separated by commas within
curly brackets, the set is said be written in Roster form.
All the above sets are written in Roster form.

Consider the set B of all multiples of 2 less than 20
B = {2, 4, 6, 8,. .........18}
We can write the multiples of 2 in the following manner
B = {18, 16, 14, 12 ,..........2} or
B = {2, 12, 4, 14, 6, 16, 8, 18, 10}
that is the order is which the elements in the set are listed is immaterial.

Consider the following example:
The set M of all the letter in the world 'mathematics'
M = {m, a, t, h, e, i c, s}
While writing the set in the Roster form, the elements are not repeated i.e, the
letters that are repeated in the word mathematics (m, a, t) are not written twice in the set.
From the above two examples we can say that when a set is written in the Roster form
(i) The order of listing the elements is immaterial
(ii) The elements in the set are not repeated.

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