PROBLEM & SOLUTION
Convert each of the following sets in the Roster Form or in the Tabular Form
Example-1) { x : x = n / ( n + 1 ), n ∈ N and n < 8 }
Ans.) As per the given condition, we can find n ∈ N and n < 8 ; so n = 1, 2, 3, 4, 5, 6, 7.
n 1 1
Then, x = -------- = -------- = ------- [ Where n = 1 ]
n + 1 1 + 1 2
n 1 1
Then, x = -------- = -------- = -------- [ Where n = 2 ]
n + 1 2 + 1 3
n 1 1
Then, x = -------- = -------- = -------- [ Where n = 3 ]
n + 1 3 + 1 4
n 1 1
Then, x = -------- = -------- = ------- [ Where n = 4 ]
n + 1 4 + 1 5
n 1 1
Then, x = -------- = -------- = -------- [ Where n = 5 ]
n + 1 5 + 1 6
n 1 1
Then, x = -------- = -------- = ------- [ Where n = 6 ]
n + 1 6 + 1 7
n 1 1
Then, x = --------- = -------- = -------- [ Where n = 7 ]
n + 1 7 + 1 8
So, the given set is x =
1 1 1 1 1 1 1
{ ------, -------, -------,------, ------, ------, ------ } (Ans.)
2 3 4 5 6 7 8
2) { x : x = 2n / ( 3n + 1 ), n ∈ N and n < 5 }
Ans.) As per the given condition, we can find n ∈ N and n < 5 ; so n = 1, 2, 3, 4
2n 2 X 1 2 1
Then, x = -------- = --------- = ------ = ------ [Where n = 1]
3n + 1 3X1+1 4 2
2n 2X2 4
Then, x = -------- = -------- = -------- [ Where n = 2 ]
3n + 1 3X2+ 1 7
2n 2 X 3 6 3
Then, x = ------- = ------- = ------- = ------- [ Where n = 3 ]
3n+ 1 3X3+ 1 10 5
2n 2X4 8 8
Then, x = -------- = -------- = ------- = ------- [ Where n = 4 ]
3n + 1 3X4 + 1 13 13
1 4 3 8
So, the given set is x = { ------ , ------, ------, ------ } (Ans.)
2 7 5 13
3) { x : x = 3r + 2 , r ∈ I and -3 ≤ r < 3 }
Ans.) As per the given condition r ∈ I and -3 ≤ r < 3,
So, r = -3, -2, -1, 0, 1, 2
If, x = 3r + 2, where r = -3, -2, -1, 0, 1, 2
So, x = 3 X ( -3 ) + 2 = - 9 + 2 = - 7
x = 3 X ( - 2 ) + 2 = - 6 + 2 = - 4
x = 3 X ( - 1 ) + 2 = - 3 + 2 = - 1
x = 3 X ( 0 ) + 2 = 0 + 2 = 2
x = 3 X 1 + 2 = 3 + 2 = 5
x = 3 X 2 + 2 = 6 + 2 = 8
hence the given set is = { -7, -4, -1, 2, 5, 8 } (Ans.)
4) { x / 4x + 5 < 25, x ∈ W }
Ans.) As per the given condition 4x + 5 < 25, x ∈ W
Since x ∈ W and we have to justify 4x + 5 < 25, so x = 0, 1, 2, 3, 4
So, the given set is x = { 0, 1, 2, 3, 4 } (Ans.)
Express each of the following set in the set-builder form –
3 4 5 6 7 8
4) { ------, -------, -------, -------, -------, ------- }
5 6 7 8 9 10
n
Ans.) { x : x = ----------, 3 ≤ n ≤ 8 and n ∈ N } (Ans.)
n + 2
5) { 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 }
Ans.) { x : x = 2n , n ∈ W and n ≤ 10 or n < 11 } (Ans.)
1 1 1 1 1
6) { -------, -------- , -------, -------- , ------- }
2 4 8 16 32
1
Ans.) { x : x = --------- , n ∈ N and n ≤ 5 } (Ans.)
2ⁿ
1 1 1 1 1 1 1 1
7) { -----, -----, -----, -----, -----, -----, -----, ----- }
1 4 9 16 25 36 49 64
1
= { x : x = -----------, n ∈ N and 1≤ n ≤ 8 } (Ans.)
n²
8) { -40, -35, -30, -25, ………….., 25 }
Ans.) { x / x = 5n, n ∈ I and -8 ≤ n ≤ 5 } (Ans.)
Express the following sets in the tabular & set builder form
1) The set ‘E’ of even natural numbers
Ans.) as per the condition if we consider the above set in tabular or roster form then the answer would be
A = { 2, 4, 6, 8, 10, 12,…………. }
as per the condition if we consider the above set in set-builder form then the answer would be -
= { x : x = 2n, n ∈ N } (Ans.)
2) The set ‘X’ of the factor of 24
Ans.) as per the condition if we consider the above set in tabular or roster form then the answer would be
X = { 1, 2, 3, 4, 6, 8, 12, 24 }
as per the condition if we consider the above set in set-builder form then the answer would be
= { x : x is factor of 24 } (Ans.)