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Exercise
1
...
Find
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Answer 1:

U ={1, 2, 3, 4, 5, 6, 7, 8, 9} A = {1, 2, 3, 4} B = {2, 4, 6, 8}

C = {3, 4, 5, 6}

( i)
( ii )
( iii )

( iv )

(v )
( vi )

1

Question 2:
If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:
(i) A = {a, b, c}
(ii) B = {d, e, f, g}
(iii)

C = {a, c, e, g}

(iv)

D = {f, g, h, a}

Answer 2:
U = {a, b, c, d, e, f, g, h}
(i) A = {a, b, c}
(i) B = {d, e, f, g}
(ii)

C = {a, c, e, g}

(iii)

D = {f, g, h, a}

Question 3:
Taking the set of natural numbers as the universal set, write down the
complements of the following sets:
(i) {x: x is an even natural number}

(ii) {x: x is an odd natural number}
(iii) {x: x is a positive multiple of 3}
(iv) {x: x is a prime number}
(v) {x: x is a natural number divisible by 3 and 5}
(vi) {x: x is a perfect square}
(vii) {x: x is perfect cube}

2

(viii) {x: x + 5 = 8} (ix) {x: 2x + 5 = 9}
(x)

{x: x ≥ 7}

(xi) {x: x

N and 2x + 1 > 10}

Answer 3:
U = N: Set of natural numbers
(i) {x: x is an even natural number}´ = {x: x is an odd natural number}
(ii) {x: x is an odd natural number}´ = {x: x is an even natural number}

(iii) {x: x is a positive multiple of 3}´= {x: x

(iv)

N and x is not a multiple of3}

{x: x is a prime number}´ ={x: x is a positive composite number and x

= 1}
(v) {x: x is a natural number divisible by 3 and 5}´ = {x: x is a natural number
that is not divisible by 3 or 5}
(vi) {x: x is a perfect square}´ = {x: x
(vii) {x: x is a perfect cube}´ = {x: x

N and x is not a perfect square}
N and x is not a perfect cube}

(viii) {x: x + 5 = 8}´ = {x: x

N and x ≠ 3}

(ix) {x: 2x + 5 = 9}´ = {x: x

N and x ≠ 2}

(x) {x: x ≥ 7}´ = {x: x
(xi) {x: x

N and x < 7}

N and 2x + 1 > 10}´ = {x: x

N and x ≤ 9/2}
3

Question 4:
If U = {1, 2, 3, 4, 5,6,7,8, 9},
A = {2, 4, 6, 8}

and

B = {2, 3, 5, 7}
...
If A is the set of all triangles with at
least one angle different from 60°, what is

?

Answer 6:
is the set of all equilateral triangles

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