Question

# Which of the following sets in Descriptive form(i) A = {a, e, i, o, u}(ii) B = {1, 3, 5, 7, 9, 11}(iii) C = {1, 4, 9, 16, 25}(iv) P = {x : x is a letter in the word ‘set theory’)(v) Q = {x : x is a prime number between 10 and 20}

Hint: To solve this question, we will first describe various forms of sets and focus on attributes of descriptive sets. Then go through the given sets one by one and see which of the given sets comply with the definition of descriptive sets.

There are three types of set representation, viz. tabular form, set builder form and descriptive form.
Tabular form: If all the elements of the set are listed between curly brackets “{}” and separated with comma “,”, such kind of set is said to be in tabular form.
Set Builder form: If the definition and condition of the set is written using various mathematical symbols and operators and enclosed between curly brackets “{}”, such kind of set is said to be in set builder form.
Descriptive form: If the definition and condition of the set is written like a statement, such a set is said to be in descriptive form.
Let us see an example:
Let A be our sample set.
Tabular form: A = {2, 4, 6, 8, 10 …}
Set Builder form: A = {x $\in N\left| \dfrac{x}{2}\in N \right.$ }
Descriptive form: A is a set of all the even numbers.
Now let us see the given sets.
(i) A = {a, e, i, o, u}
(ii) B = {1, 3, 5, 7, 9, 11}
(iii) C = {1, 4, 9, 16, 25}
(i), (ii) and (iii) are in tabular form.
(iv) P = {x : x is a letter in the word ‘set theory’)
(v) Q = {x : x is a prime number between 10 and 20}
Both set P and Q are in set builder form.
Thus, there are no sets in descriptive form.

Note: In the sets P and Q, even though the statements are descriptive, they are enclosed in curly brackets and that’s what makes them examples of set builder form and not descriptive form.