Question

Describe the following sets in Roster form:

(i) {x : x is a letter before e in the English alphabet}

(ii) {x ∈ N: x² < 25}

(iii) {x ∈ N: x is a prime number, 10 < x < 20}

(iv) {x ∈ N: x = 2n, n ∈ N}

(v) {x ∈ R: x > x}

(vi) {x : x is a prime number which is a divisor of 60}

(vii) {x : x is a two digit number such that the sum of its digits is 8}

(viii) The set of all letters in the word ‘Trigonometry’

(ix) The set of all letters in the word ‘Better.’

Answer 1

(i) {x : x is a letter before e in the English alphabet}

Therefore, when we read whole sentence it becomes x is such that x is a letter before ‘e’ in the English alphabet. Then letters before ‘e’ are a,b,c,d.

∴ Roster form will be {a,b,c,d}.

(ii) {x ∈ N: x² < 25}

x ∈ N that implies x is a natural number.

x² < 25

x < ±5

Here, as x belongs to the natural number that means x < 5.

Here, also all numbers less than 5 are 1,2,3,4.

∴ Roster form will be {1,2,3,4}.

(iii) {x ∈ N: x is a prime number, 10 < x < 20}

Here, X is a natural number and is between 10 and 20.

Since, X is such that X is a prime number between 10 and 20.

Prime numbers between 10 and 20 are 11,13,17,19.

∴ Roster form will be {11,13,17,19}.

(iv) {x ∈ N: x = 2n, n ∈ N}

X is a natural number also x = 2n

Hence, roster form will be {2,4,6,8…..}.

This an infinite set.

(v) {x ∈ R: x > x}

Any real number is equal to its value it is neither less nor greater.

Therefore, Roster form of such real numbers which has value less than itself has no such numbers.

∴ Roster form will be ϕ. This is called a null set.

(vi) {x : x is a prime number which is a divisor of 60}

All numbers which are divisor of 60 are = 1,2,3,4,5,6,10,12,15,20,30,60.

Then, prime numbers are = 2, 3, 5.

Hence, roster form will be {2, 3, 5}.

(vii) {x : x is a two digit number such that the sum of its digits is 8}

Here, numbers which have sum of its digits as 8 are = 17, 26, 35, 44, 53, 62, 71, 80

Hence, roster form will be {17, 26, 35, 44, 53, 62, 71, 80}.

(viii) The set of all letters in the word ‘Trigonometry’

Since, as repetition is not allowed in a set, now the distinct letters are

Trigonometry = t, r, i, g, o, n, m, e, y

Hence, roster form will be {t, r, i, g, o, n, m, e, y}

(ix) The set of all letters in the word ‘Better.’

Since, as repetition is not allowed in a set, now the distinct letters are

Better = b, e, t, r

Hence, roster form will be {b, e, t, r}