Question

Write the following sets in the roster form:

a) The set of prime numbers less than 15.

b) The set of colours of the rainbow.​

Answer 1

ANSWER :

(a) Suppose the set of the Prime number less than 15 is Set P.

• In roaster method, the Set P will be :-

➺ P = { 1, 3, 5, 7, 11, 13 }

(b) Suppose the set of the Colours of the Rainbow is Set C.

• In roaster method, the Set C will be :-

➺ C = { Red, Orange, Yellow, Green, Blue, Indigo, Violet }

MORE INFORMATION :

➣ Set :-

➯ In the later part of 19th century, George Cantor, a German mathematician introduced Set Theory ad a new discipline of mathematics.

• According to Cantor's concept, "A set is a collection of well defined and distinct objects". The word well defined means that given any object it must be possible to tell beyond doubt whether that object belongs to the collection or not and the word distinct means that no two elements of the set are same.

➯ The objects which are listed in a set are called the elements of a set. A set is usually denoted by a Capital Letter of English alphabet, while the elements of a set is usually denoted by Small Letters of English alphabet.

➣There are two methods used for representation of Set :-

• [1] Tabular or Roaster Method : In the Tabular or Roaster Method, the elements of a set are listed in any order with the braces { }, being separated by commas (,). For example:- If N is a set of natural numbers less than 5, then it is written as : N = { 1, 2, 3, 4 } or V = { 4, 2, 1, 3}.

• [2] Set Builder or Rule Method : In the Set Builder or Rule Method, x is used to represent the elements of the set which satisfy a definite property say P (x) and the set is expressed symbolically as { x : P (x) } or { x | P (x) }, that means, the set of all those elements x which satisfies property P (x). For example :- If N is the set of natural numbers less than 5 , then it is written as : N = { x : x is a natural number less than 5 } or V = { x | x is a natural number less than 5}.