Describe the following sets in Roster form :
(i) {x : x is a letter before e in the English alphabet}.
(ii) {x ϵ N:x2<25}
(iii) {x ϵ N: x is a prime number, 10 < x < 20}.
(iv) x ϵ N:x=2n,nϵN.
(v) x ϵ R:x>x.
(vi) {x : x is a prime number which is a divisor of 60}
(vii) {x : x ix 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'.
Describe the following sets in Roster form :
(i) {x : x is a letter before e in the English alphabet}.
(ii) {x ϵ N:x2<25}
(iii) {x ϵ N: x is a prime number, 10 < x < 20}.
(iv) x ϵ N:x=2n,nϵN.
(v) x ϵ R:x>x.
(vi) {x : x is a prime number which is a divisor of 60}
(vii) {x : x ix 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'.
(i) In Roster form, we describe a set by listing its elements, separated by commas and the elements are written within braces { }. If a set has infinitely many elements, then comma is followed by ....., where the dots stand for 'and so on '.
The above set in Roster form can be written as {a, b, c, d}. Since the letters a,b,c and d precedes e in the english alphabet.
(ii) In Roster form, we describe a set by listing its elements, separated commas and the elements are written within braces { }. If a set has infinitely many elements, then comma is followed by ....., where the dots stand for 'and so on'.
1 ϵ N∵12=1<252 ϵ N∵22=4<253 ϵ N∵32=9<254 ϵ N∵42=16<25
Hence, the above set can be written as {1,2,3,4}
(iii) In Roster form, we describe a set by lisiting its elements, separated by commas and the elements are written within braces { }. If a set has infinitely many elements, then comma is followed by ....., where the dots stand for 'and so on '.
We note that a < x < b means that x is more than a but less than b.
The prime numbers which are more than 10 fact less than 20 are 11, 13, 17 and 19. Hence the above set can be written as {11, 13, 17, 19}
(iv) In Roster form, we describe a set by lisiting its elements, separated by commas and the elements are written within braces { }. If a set has infinitely many elements, then comma is followed by ...., where the dots stand for 'and so on'.
The above set can be written as {2, 4, 6, 8...} since all those natural numbers, which can be written as a multiple of 2 are the even natural numbers.
(v) In Roster form, we describe a set by lisiting its elements, separated by commas and the elements are written within braces { }. If a set has infinitely many elements, then comma is followed by ..., where the dots stand for 'and so on'.
We know that given any x ϵ R , x is always less than or equal to itself, i.e. x<––x Hence the above set is empty, i.e, ϕ.
(vi) In Roster form. we describe a set by listing its elements, separated by commas and the elements are written within braces { }. If a set has infinitely many elements, then comma is followed by ...., where the dots stand for 'and so on '.
The prime divisors of 60 are 2, 3, 5.
Hence the above set can be written as {2, 3, 5}.
(vii) In Roster form, we describe a set by listing its elements, separated by commas and the elements are written within braces { }. If a set has infinitely many elements, then comma is followed by ...., where the dots stand for 'and so on '.
The above set can be written as
{17,26,35,44,53,62,71,80}.
(viii) In Roster form, we describe a set by listing its elements, separated by commas and the elements are written within braces { }. If a set has infinitely many elements, then comma is followed by ...., where the dots stand for 'and so on '.
As repetition is not allowed in a set, the distinct letter are T, R, I, G, O N, M, E, Y.
Hence the above set can be written as
{T, R, I, G, O, N, M, E, Y}.
(ix) In Roster form, we describe a set by listing its elements, separated by commas and the elements are written within braces { }. If a set has infinitely many elements, then comma is followed by ...., where the dots stand for 'and so on '.
The distinct letters are B, E, T, R.
Hence the set can be written as {B, E, T, R}.
(i) In Roster form, we describe a set by listing its elements, separated by commas and the elements are written within braces { }. If a set has infinitely many elements, then comma is followed by ....., where the dots stand for 'and so on '.
The above set in Roster form can be written as {a, b, c, d}. Since the letters a,b,c and d precedes e in the english alphabet.
(ii) In Roster form, we describe a set by listing its elements, separated commas and the elements are written within braces { }. If a set has infinitely many elements, then comma is followed by ....., where the dots stand for 'and so on'.
1 ϵ N∵12=1<252 ϵ N∵22=4<253 ϵ N∵32=9<254 ϵ N∵42=16<25
Hence, the above set can be written as {1,2,3,4}
(iii) In Roster form, we describe a set by lisiting its elements, separated by commas and the elements are written within braces { }. If a set has infinitely many elements, then comma is followed by ....., where the dots stand for 'and so on '.
We note that a < x < b means that x is more than a but less than b.
The prime numbers which are more than 10 fact less than 20 are 11, 13, 17 and 19. Hence the above set can be written as {11, 13, 17, 19}
(iv) In Roster form, we describe a set by lisiting its elements, separated by commas and the elements are written within braces { }. If a set has infinitely many elements, then comma is followed by ...., where the dots stand for 'and so on'.
The above set can be written as {2, 4, 6, 8...} since all those natural numbers, which can be written as a multiple of 2 are the even natural numbers.
(v) In Roster form, we describe a set by lisiting its elements, separated by commas and the elements are written within braces { }. If a set has infinitely many elements, then comma is followed by ..., where the dots stand for 'and so on'.
We know that given any x ϵ R , x is always less than or equal to itself, i.e. x<––x Hence the above set is empty, i.e, ϕ.
(vi) In Roster form. we describe a set by listing its elements, separated by commas and the elements are written within braces { }. If a set has infinitely many elements, then comma is followed by ...., where the dots stand for 'and so on '.
The prime divisors of 60 are 2, 3, 5.
Hence the above set can be written as {2, 3, 5}.
(vii) In Roster form, we describe a set by listing its elements, separated by commas and the elements are written within braces { }. If a set has infinitely many elements, then comma is followed by ...., where the dots stand for 'and so on '.
The above set can be written as
{17,26,35,44,53,62,71,80}.
(viii) In Roster form, we describe a set by listing its elements, separated by commas and the elements are written within braces { }. If a set has infinitely many elements, then comma is followed by ...., where the dots stand for 'and so on '.
As repetition is not allowed in a set, the distinct letter are T, R, I, G, O N, M, E, Y.
Hence the above set can be written as
{T, R, I, G, O, N, M, E, Y}.
(ix) In Roster form, we describe a set by listing its elements, separated by commas and the elements are written within braces { }. If a set has infinitely many elements, then comma is followed by ...., where the dots stand for 'and so on '.
The distinct letters are B, E, T, R.
Hence the set can be written as {B, E, T, R}.
