Question -
Answer -
(i) {x: x is a letter before e in the English alphabet}
So, when we read whole sentence it becomes x is such that x is a letterbefore ‘e’ in the English alphabet. Now letters before ‘e’ are a,b,c,d.
∴ Rosterform will be {a,b,c,d}.
(ii) {x ∈N: x2 < 25}
x ∈ N that implies x is a natural number.
x2 < 25
x < ±5
As x belongs to the natural number that means x < 5.
All numbers less than 5 are 1,2,3,4.
∴ Rosterform will be {1,2,3,4}.
(iii) {x∈ N:x is a prime number, 10 < x < 20}
X is a natural number and is between 10 and 20.
X is such that X is a prime number between 10 and 20.
Prime numbers between 10 and 20 are 11,13,17,19.
∴ Rosterform will be {11,13,17,19}.
(iv) {x∈ N:x = 2n, n ∈ N}
X is a natural number also x = 2n
∴ Rosterform 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.
So, Roster form of such real numbers which has value less than itself hasno such numbers.
∴ Rosterform 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.
Now, prime numbers are = 2, 3, 5.
∴ Rosterform will be {2, 3, 5}.
(vii) {x: x is a two digit number such that the sum of its digits is 8}
Numbers which have sum of its digits as 8 are = 17, 26, 35, 44, 53, 62,71, 80
∴Roster form will be {17, 26, 35, 44, 53, 62, 71, 80}.
(viii)The set of all letters in the word ‘Trigonometry’
As repetition is not allowed in a set, then the distinct letters are
Trigonometry = t, r, i, g, o, n, m, e, y
∴ Rosterform will be {t, r, i, g, o, n, m, e, y}
(ix)The set of all letters in the word ‘Better.’
As repetition is not allowed in a set, then the distinct letters are
Better = b, e, t, r
∴ Rosterform will be {b, e, t, r}