HOW TO REPRESENT TJE GIVEN STATEMENT IN ROSTER FORM

Listing the elements of a set inside a pair of braces { } is called the roster form.

Question 1 :

Write the following in roster form.

(i) {x ∈ N : x² < 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 x²  =  4 < 121 (ture)

If x = 3, then x²  =  9 < 121 (ture)

We should not take 4, because it is composite not prime.

If x = 5, then x²  =  25 < 121 (ture)

If x = 7, then x²  =  49 < 121 (ture)

If x = 11, then x²  =  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)(x² − 1) = 0.

Solution :

Let f(x)  =  (x − 1)(x + 1)(x² − 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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