How to Represent the Given Statement in Roster Form ?
Here we are going to see how to represent the given statement in roster form.
Roster form :
Listing the elements of a set inside a pair of braces { } is called the roster form.
To understand the concept even more better, let us look into some examples.
Question 1 :
Write the following in roster form.
(i) {x ∈ N : x^{2} < 121 and x is a prime}.
Solution :
The required set will contain only prime numbers and whose squares must be lesser than 121.
If x = 2, then x^{2} = 4 < 121 (ture)
If x = 3, then x^{2} = 9 < 121 (ture)
We should not take 4, because it is composite not prime.
If x = 5, then x^{2} = 25 < 121 (ture)
If x = 7, then x^{2} = 49 < 121 (ture)
If x = 11, then x^{2} = 121 < 121 (false)
Hence the required set is {2, 3, 5, 7}
(ii) the set of all positive roots of the equation (x − 1)(x + 1)(x^{2} − 1) = 0.
Solution :
Let f(x) = (x − 1)(x + 1)(x^{2} − 1)
If x = 1, then f(1) will become 0.
If x = -1, then f(-1) will become 0, but the required set must contain positive values.
Hence the required set is {1}.
(iii) {x ∈ N : 4x + 9 < 52}.
Solution :
N means set of natural numbers.
f(x) = 4x + 9 < 52
If x = 1, f(1) = 4(1) + 9 ==> 13 < 52
If x = 2, f(2) = 4(2) + 9 ==> 17 < 52
If x = 3, f(3) = 4(3) + 9 ==> 21 < 52
If x = 4, f(4) = 4(4) + 9 ==> 25 < 52
If x = 5, f(5) = 4(5) + 9 ==> 29 < 52
If x = 6, f(6) = 4(6) + 9 ==> 33 < 52
If x = 7, f(7) = 4(7) + 9 ==> 37 < 52
If x = 8, f(8) = 4(8) + 9 ==> 41 < 52
If x = 9, f(9) = 4(9) + 9 ==> 45 < 52
If x = 10, f(10) = 4(10) + 9 ==> 49 < 52
If x = 11, f(11) = 4(11) + 9 ==> 53 < 52 (False)
Hence the required set is {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(iv) {x : (x−4)/(x+2) = 3, x ∈ R − {−2}}.
Solution :
Let f(x) = (x−4)/(x+2) = 3
x - 4 = 3(x + 2)
x - 4 = 3x + 6
x - 3x = 6 + 4
-2x = 10
x = -5
Hence the required set is {-5}.
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