Question

Write the following set in roster form: D = \\{ all letters in the word PERMISSION \\}

Answer 1

We will use the definition of a roster form of a set. Using this definition, we will express the set $D$ in roster form. In mathematics, a set is defined as an organised collection of objects or elements that can be represented in set builder form as well as in roaster form.

Complete step by step solution:
We are given the set D = \\{ all letters in the word PERMISSION \\} . We are supposed to express the set $D$ in roster form. Roster form (or) Tabular form is a representation of a set that lists all the elements of the set. These elements have to be separated by commas and enclosed within braces. In this representation, the elements that are repeated can be listed out only once.
Let us write all the letters of the word “PERMISSION” in alphabetical order.
The letters are E, I, I, M, N, O, P, R, S, S.
We see that the letter “E” occurs only once. So, “E” is included in the set. The letter “I” appears twice. But while expressing the set in roster form, we will include “I” only one time. Now, the letters “M”, “N”, “O”, “P” and “R” appear only once. Again, the letter “S” appears twice. In roster form, we will include it in the set only once.

Therefore, the set $D$ is expressed in roster form as D = \\{ E, I, M, N, O, P, R, S \\}

Note:
Another way of expressing a set is by set-builder notation. In this method, elements of the set are defined by using mathematical statements. The above set can be written in set-builder notation as D = \\{ x|x is a letter of the word “PERMISSION” \\}