One way to specify a set is to give a verbal description of its elements. This is known as the Descriptive form of specification.
The description must allow a concise determination of which elements belong to the set and which elements do not.
Let us look into some examples to understand how to write the given set in descriptive form.
Example 1 :
Write the following set in descriptive form.
A = {a, e, i, o, u}
Solution :
The given set contains vowels. So, we can represent the above set in descriptive form as follows.
A is the set of all vowels in the English alphabet
Example 2 :
Write the following set in descriptive form.
B = {1, 3, 5, 7, 9, 11}
Solution :
The given set contains odd numbers. But it ends with 11. So, we can represent the above set in descriptive form as follows.
B is the set of all odd natural numbers less than or equal to 11
Example 3 :
Write the following set in descriptive form.
C = {1, 4, 9, 16, 25}
Solution :
The given set contains the square of natural numbers. But it ends with 25. So, we can represent the above set in descriptive form as follows.
C is the set of all square numbers less than 26.
Example 4 :
Write the following set in descriptive form.
P = {x : x is a letter in the word ‘set theory’}
Solution :
The given set is in set builder form. It contains the letters of the word "set theory".
P is the set of all letters in the word ‘set theory’
Example 5 :
Write the following set in descriptive form.
Q = {x : x is a prime number between 10 and 20}
Solution :
The given set is in set builder form. It contains the prime numbers between 10 and 20.
Q is the set of all prime numbers between 10 and 20
Example 6 :
Write the following set in descriptive form.
Q = {1, 2, 3, 4, 5, 6}
Solution :
The given set contains the set of natural numbers. But it ends with 6. So, we can represent the above set in descriptive form as follows.
Q is the set of natural numbers less than 7.
Example 7 :
Write the following set in descriptive form.
R = {2, 4, 6, 8, ...................}
Solution :
The given set contains the set of even numbers. . So, we can represent the above set in descriptive form as follows.
R is the set of even numbers.
Example 8 :
Write the following set in descriptive form.
S = {3, 6, 9, 12, ...................}
Solution :
The given set contains multiples of 3. So, we can represent the above set in descriptive form as follows.
S is the multiples of 3.
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