Question

Represent the following set in roster method: The set of letters in the word ELEPHANT.

Answer 1

Hint: Read the definition of set and its two types, that is set – builder form and roster form. Check out the properties of these forms and the difference between them to write the set of letters of the given word in roster form. Write all the different letters of the given word inside { } and use commas to separate two letters.

Complete step by step answer:
Here, we have to represent the set of letters in the word ELEPHANT in roster form. Let us first see the definition of set and its types of representation.
In mathematics, a set is a well – defined collection of distinct objects. The objects that make up a set, also known as the set’s elements or members. These elements can be anything: numbers, people, letters of the alphabet, other sets and so on. There are two ways of representing members of a ser.
1. Roster form: -
The roster notation method of defining a set consists of listing each member of the set. In this form the set is denoted by enclosing the lost of members in curly brackets:
A = {M, N, O, P, R}
If in a word, any repetition of a letter is there then we write that letter only once in the set. For example: let us take the word MIRROR. In roster form it can be written as: {M, I, R, O}. Remember that the letters can be written in any order.
2. Set – builder form: -
In set builder form, the set is specified as a selection from a larger set, determined by a condition involving the elements. For example, a set A can be specified as follows: -
A = {n : n is an integer, and \[0\le n\le 5\]}
Here, the colon (:) means “such that”.
Now, let us come to the question. We have the word ELEPHANT and it is to be represented as a roster form. Here, E is repeating twice so we have to write it once. Let us assume the set of the letters as set X.
\[\Rightarrow \] X = {E, L, P, H, A, N, T}

Note: One must note that we have to use curly braces { } in roster form. If we will use small brackets ( ) or square brackets [ ] then it will be a wrong notation. You must not forget to separate the letters with commas. Remember that if we will write the repeated letter of a word inside the bracket then also it will not be considered wrong but generally we write the repeated letter once.