Question

Write the following sets in the roster form.
1. A = {x : x ∈ W, x ≤ 5}
2. B = {x : x ∈ I, -3 < x < 3)
3. C = {x : x is divisible by 12}
4. D = {x : x = 3p, p ∈ W, p ≤ 3}
5. E = {x : x = a2, a ∈ N, 3 < a < 7}
6. F = {x : x = n/(n + 1), n ∈ N and n ≤ 4}

Answer 1

A = ( 0 , 1 , 2 , 3 , 4 , 5 )

B = ( - 2 , - 1 , 0 , 1 , 2 )

C = ( 1 , 2 , 3 , 4 , 6 , 12 )

D = ( 0 , 3 , 6 , 9 )

E = ( 16 , 25 , 36 )

Hope this answer helps you friend ♥️

Answer 2

A = {0, 1, 2, 3, 4, 5}

B = {- 2, -1, 0, 1, 2 }

C = {12, 24, 36, 48 ... }

D = {0, 3, 6, 9}

E = { 16, 25, 36 }

F = { 1/2, 2/3, 3/4, 4/5 }

Given:

Set builder forms of sets are

1. A = {x : x ∈ W, x ≤ 5}

2. B = {x : x ∈ I, -3 < x < 3)

3. C = {x : x is divisible by 12}

4. D = {x : x = 3p, p ∈ W, p ≤ 3}

5. E = {x : x = a2, a ∈ N, 3 < a < 7}

6. F = {x : x = n/(n + 1), n ∈ N and n ≤ 4}

To find:

Roster forms of given sets

Solution:

1. A = {x : x ∈ W, x ≤ 5}

Here, x is belongs to whole numbers and x is less and equal to 5

As we know whole number (W) = {0, 1, 2 .... }

⇒ A = {0, 1, 2, 3, 4, 5}

2. B = {x : x ∈ I, -3 < x < 3)

Here, x belongs to integers and x is greater than -3 and less than 3

As we know integers I = {... -2, -1, 0, 1, 2... }

⇒ B = {- 2, -1, 0, 1, 2 }

3. C = {x : x is divisible by 12}

Here, x is divisible by 12 then set C = multiples of 12

⇒ C = {12, 24, 36, 48 ... }

4. D = {x : x = 3p, p ∈ W, p ≤ 3}

Here, x = 3p , p belongs to Whole numbers and p is less and equal to 3

then p values are 0, 1, 2, 3

when p = 0 ⇒ x = 3(0) = 0

when p = 1 ⇒ x = 3(1) = 3

when p = 2 ⇒ x = 3(2) = 6

when p = 3 ⇒ x = 3(3) = 9  

⇒ D = {0, 3, 6, 9}

5. E = {x : x = a², a ∈ N, 3 < a < 7}

Here, x = a² where a is natural number, a is greater than 3 and less than 7

Then a values are 4, 5, 6

When a = 4 ⇒ x = 4² = 16

When a = 5 ⇒ x = 5² = 25

When a = 6 ⇒ x = 6² = 36

⇒ E = { 16, 25, 36 }

6. F = {x : x = n/(n + 1), n ∈ N and n ≤ 4}

Here, x = n/(n + 1) where n is less than and equal to 4  

Then n values are 1, 2, 3, and 4

When n = 1 ⇒ x = 1/1+1 = 1/2

When n = 2 ⇒ x = 2 /2+1 = 2/3

When n = 3 ⇒ x =3 /3+1 = 3/4

When n = 4 ⇒ x = 4/4+1 = 4/5

⇒ F = { 1/2, 2/3, 3/4, 4/5 }

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