Question

Describe the following set in Roster form:
{x: x is a letter before e in the English alphabet system}

Answer 1

Hint: In this question, we have given a set in the set builder form and we have been asked to describe the same in the roster form. Therefore, we should understand the roster method of representing a set, find out all the elements of the set which satisfy the given condition and then use the elements to write the given set in the set builder form.

Complete step-by-step answer:
In this method we have to convert the set from set builder form to Roster form. Therefore, we should first understand the definition of the set builder and roster form which are as follows:
a)In the set builder form, the property which an element in the set satisfies is specified by writing a variable followed by a colon and then the property satisfied by the variable. Thus, the variable can take all the values which satisfy the property and thus all such values of the variables will be elements of the set. For example, in the set
{x: property of x}
all values of x which satisfy the given condition will be part of the set……………… (1.1)

b)In the roster form, all the elements of the set are written explicitly within curly braces with the elements separated by a comma. For example, if a, b, c, d and e are elements of the set A, then it can be represented as
A={a,b,c,d,e}………………………… (1.2)
In this question, the given set is
S= {x: x is a letter before e in the English alphabet system}
Now, we know that only the letters a,b,c and d appear before e in the English alphabet system and thus S will contain only a,b,c and d. Therefore, using the definition (1.2), we can write the given set in roster form as
S= {x: x is a letter before e in the English alphabet system} = {a,b,c,d}
Thus, {a,b,c,d} is the description of the set in roster form and is the answer to this question.

Note: In this set all the letters before e are asked, therefore we should be careful not to include e as the element of the set as it does not appear before itself.