Chapter 1: Sets – Exercise 1.2

Sets – Exercise 1.2 – Q.1(i)

In Roster form, we describe a set by listing its elements, reparated by commas and the elements are written within braces { }. If a set has infinitely many elements, them 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.

Sets – Exercise 1.2 – Q.1(ii)

In Roster form, we describe a set by listing its elements, reparated by commas and the elements are written within braces { }. If a set has infinitely many elements, them comma is followed by ..., where the dots stand for 'and so on'.

1 ϵ N ∵ 1² = 1 < 25

2 ϵ N ∵ 2² = 4 < 25

3 ϵ N ∵3² = 9 < 25

4 ϵ N ∵ 4² = 16 < 25

Hence , the above set can be written as {1, 2, 3, 4}

Sets – Exercise 1.2 – Q.1(iii)

In Roster form, we describe a set by listing its elements, reparated by commas and the elements are written within braces (}. If a set has infinitely many elements, them comma is followed by ..., where the dots stand for 'and so on'.

We note that a < x < b m sans tha 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, 191}

Sets – Exercise 1.2 – Q.1(iv)

In Roster form, we describe a set by listing its elements, reparated by commas and the elements are written within braces (}.If a set has infinitely many elements, them 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.

Sets – Exercise 1.2 – Q.1(v)

In Roster form, we describe a set by listing its elements, reparated by commas and the elements are written within braces { }. If a set has infinitely many elements, them 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. ∅.

Sets – Exercise 1.2 – Q.1(vi)

In Roster form, we describe a set by listing its elements, reparated by commas and the elements are written within braces { }. If a set has infinitely many elements, them 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}

Sets – Exercise 1.2 – Q.1(vii)

In Roster form, we describe a set by listing its elements, reparated by commas and the elements are written within braces (}. If a set has infinitely many elements, them 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}

Sets – Exercise 1.2 – Q.1(viii)

In Roster form, we describe a set by listing its elements, reparated by commas and the elements are written within braces { }. Ifa set has infinitely many elements, them comma is followed by ..., where the dots stand for 'and so on'.

As repetition is not allowed in a set, the distinct letters 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}

Sets – Exercise 1.2 – Q.1(ix)

In Roster form, we describe a set by listing its elements, reparated by commas and the elements are written within braces {}. If a set has infinitely many elements, them 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.}

Sets – Exercise 1.2 – Q.2(i)

In set Builder form, a set is described by some characterizing property P (x) of its elements x.

In this case a set can be described as {x : P (x)hold} or {x|P{x} holds} which is read as 'the set of all x such that P (x) holds'.

The symbols ∵ or 'I' is read as 'such that'.

So the above set A in Set-Builder form may be written as

A = {x ϵ N:x < 7}

i .e A is the set of natural numbers x such that x is less than 7.

Or

A = {x ϵ N |1 < x < 6},

i.e A is the set of natural numbers x such that x is

greater than or equal 1 and less than or equal to 6.

Sets – Exercise 1.2 – Q.2(ii)

In set Builder form, a set is described by some characterizing property P(x) of its elements x.

In this case a set can be described as {x : P(x) hold} or {x|P(x) holds} which is read as 'the set of all x such that P (x) holds'.

The symbols ':' or 'I' is read as 'such that'.

i.e B is the set of all those x such that x = 1/n, where n ϵ N

Sets – Exercise 1.2 – Q.2(iii)

In set Builder form, a set is described by some characterizing property P(x) of its elements x.

In this case a set can be described as {x : P (x) hold} or {x|P(x) holds} which is read as 'the set of all x such that P(x) holds'.

The symbols ':' or 'I' is read as 'such that'.

C = {x : x = 3k, k ϵ Z⁺, the set of positive integers},

i.e. C is the set of multiples of 3 including 0

Sets – Exercise 1.2 – Q.2(iv)

In set Builder form, a set is described by some characterizing property P(x) of its elements x.

In this case a set can be described as {x : P(x) hold} or {x|P(x) holds} which is read as 'the set of all x such that P (x) holds'.

The symbols ':' or 'I' is read as 'such that'.

D = {x ϵ N: 9 < x < 16},

i.e. D is the set of natural numbers which are more than 9 but less than 16.

Sets – Exercise 1.2 – Q.2(v)

(v) In set Builder form, a set is described by some characterizing property P (x) of its elements x.

In this case a set can be described as : {x: P(x) hold} or {x I P(x)holds} which is read as 'the set of all x such that P (x) holds'.

The symbols ':' or 'I' is read as 'such that'.

E = {x ϵ Z : -1 < x < 1}

Or

E = {x ϵ Z: x = 0}

Sets – Exercise 1.2 – Q.2(vi)

In set Builder form, a set s described by some characterizing property P (x) of its elements x.

In this case a set can be described as {x: P(x) hold} or {x I P(x) holds} which is read as 'the set of all x such that P (x) holds'.

The symbols ':' or 'I' is read as 'such that'.

As 1² = 1

2² = 4

3² = 9

:

:

10² = 100

∴ The above set may be described as

{x² : x ϵ N 8c 1 ≤ x ≤ 10}