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Mathematics

Given the universal set = { x : x ∈ N and x < 20}, find :

(i) A = {x : x = 3p ; p ∈ N}

(ii) B = {y : y = 2n + 3, n ∈ N}

(iii) C = {x : x is divisible by 4}

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Answer

(i) x = 3p

When p = 1

x = 3p = 3 x 1 = 3

When p = 2

x = 3p = 3 x 2 = 6

When p = 3

x = 3p = 3 x 3 = 9

When p = 4

x = 3p = 3 x 4 = 12

When p = 5

x = 3p = 3 x 5 = 15

When p = 6

x = 3p = 3 x 6 = 18

A = {3, 6, 9, 12, 15, 18}

(ii) y = 2n + 3

When n = 1

y = 2n + 3 = 2 x 1 + 3 = 5

When n = 2

y = 2n + 3 = 2 x 2 + 3 = 7

When n = 3

y = 2n + 3 = 2 x 3 + 3 = 9

When n = 4

y = 2n + 3 = 2 x 4 + 3 = 11

When n = 5

y = 2n + 3 = 2 x 5 + 3 = 13

When n = 6

y = 2n + 3 = 2 x 6 + 3 = 15

When n = 7

y = 2n + 3 = 2 x 7 + 3 = 17

When n = 8

y = 2n + 3 = 2 x 8 + 3 = 19

B = {5, 7, 9, 11, 13, 15, 17, 19}

(iii) x is divisible by 4.

x = 4, 8, 12, 16

C = {4, 8, 12, 16}

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