PROBLEM & SOLUTIONS OF SET
Example –1
Let Y = { x /x = 2n+1, n ϵ Y, 4 < n < 16 } , write ‘Y’ by the roster method and find n(Y)
Ans.) Condition given here, 2n+1 , n ϵ Y , 4 < n < 16.
So, 2n + 1 = 2*2 +1, 2*3+1, 2*4 + 1, 2*4 + 1, 2*5 +1, 2*6 + 1, 2*7 + 1 = 5, 7, 9, 11, 13, 15
( n= 1, 2, 3, 4,……... )
So, Y = { 5, 7, 9, 11, 13, 15 }, as there are 6 members in the set ‘Y’, n(Y) = 6
Example – 2
Write the Set Z = { 7, 9, 11, 13, 15, 17, 19 } by the Rule method
Ans.) Each member of the set is an Odd natural number and no number is greater than 19 and less than 7, So n = 2n +1, (7< n < 19)
Z = x/x = 2n + 1, n ϵ Z , 7 < n < 19
Example – 3
Write the following sets in tabular & set builder form; The set ‘Z’ of even natural number between 2 to 15.
In tabular form, Z = { 4, 6, 8, 10, 12, 14 }
In Set-builder form, Z = { x / x , 2n + 2 , n ϵ Z, 2 < n < 15 }
Example – 4
Write the following set ‘X’ of consonant from the word “ HOSPITAL ”
In tabular form, X = { H, S, P, T, L }
In Set-builder form, X = { x/ x is a consonant in the word HOSPITAL }
Example – 5
Write the following set ‘X’ of the vowel from the word “ HOSPITAL ”
In a tabular form, X = { O, I, A }
In Set-builder form, X = { x/ x is a vowel in the word HOSPITAL }