Question

Describe the following sets in the roaster form:
$({\text{i)}}$ {x/x is a letter of the word ‘MARRIAGE’}
$(i{\text{i)}}$ {x/x is an integer and $ - \dfrac{1}{2} < x < \dfrac{9}{2}$}
$(ii{\text{i)}}$ {x/x = 2n, x$ \subset $N}

Answer 1

Hint- Here, we will first of all see what exactly is a roaster form representation of any set. Then, we will find all the elements of the sets given in the problem. Then, we will separate these elements using commas and enclose them in enclosed braces {} to have roaster form.

Complete Step-by-Step solution:
Roaster form is a method of representation of a set.
In roaster form, all the elements of a set are listed, the elements are being separated by commas and are enclosed within braces {}.
We have to represent the given sets in the roaster form
$({\text{i)}}$ Let set A corresponds to the set {x/x is a letter of the word ‘MARRIAGE’}
In the word ‘MARRIAGE’, the different letters included are M,A,R,I,G and E. In this word, the letter A and R are repeated twice and hence, 1 A and 1 R is neglected while representation.
Set A = {M,A,R,I,G,E}
The above set represents the set {x/x is a letter of the word ‘MARRIAGE’} in roaster form.
$(i{\text{i)}}$ Let set B corresponds to the set {x/x is an integer and $ - \dfrac{1}{2} < x < \dfrac{9}{2}$}
Since, we know that the integers which lies between $ - \dfrac{1}{2}$ and $\dfrac{9}{2}$ or the integers which are greater than $ - \dfrac{1}{2} = - 0.5$ and less than $\dfrac{9}{2} = 4.5$ are 0,1,2,3 and 4
Therefore, set B will include 0,1,2,3 and 4 as its elements
Set B = {0,1,2,3,4}
The above set represents the set {x/x is an integer and $ - \dfrac{1}{2} < x < \dfrac{9}{2}$} in roaster form.
$(ii{\text{i)}}$ Let set C corresponds to the set {x/x = 2n, x$ \subset $N} where N represents the set of natural numbers (natural numbers are the numbers starting from 1 up to positive infinity)
Since, x$ \subset $N means that x belongs to the set of natural numbers
x = 1,2,3,4,5,….,n [up to n]
(2n) Elements are x = 2,4,6,8,10,…..,2n
Therefore, set C = {2,4,6,8,10,…,2n} where n is any natural number
The above set represents the set {x/x = 2n, x$ \subset $N} in roaster form.

Note- Apart from the roaster form of representation of any set, there also exists a set-builder form which is another form of representation. In the set-builder form, all the elements of the set must possess a single property to become the member of that set. In the problem, the given sets are represented in set-builder form.