**Question 1**:

List
all the subsets of set

*P*= {*r*,*s*}.

*Solution:*
There
are 2 elements, so the number of subsets of set

*P*is 2*= 2*^{n}^{2}= 4.
Set

*P*= {*r*,*s*}
Therefore

**subsets of set***P*= {*r*}, {*s*}, {*r*,*s*}, {*}.***Question 2**:

Diagram
above shows a Venn diagram with the universal set, ξ =

*Q*υ*P.*
List
all the subset of set

*P*.

*Solution:*
Set

*P*has 3 elements, so the number of subsets of set*P*is 2*= 2*^{n}^{3}= 8.
Set

*P*= {2, 3, 5}
Therefore

**subsets of set***P*= {*}, {2}, {3}, {5}, {2, 3}, {2, 5}, {3, 5},***{2, 3, 5}.**

**Question 3**:

It
is given that the universal set, ξ = {

set

number}.

*x*: 30 ≤*x*< 42,*x*is an integer} andset

*P*= {*x*:*x*is a number such that the sum of it its two digits is an evennumber}.

Find
set

*P*’.

*Solution:*
ξ
= {30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41}

*P*= {31, 33, 35, 37, 39, 40}

Therefore

*P’*= {30, 32, 34, 36, 38, 41}.**Question 4**:

Given
that universal set ξ = {

*x*: 3 <*x*≤ 16,*x*is an integer},
Set

*A*= {4, 11, 13, 16},
Set

*B*= {*x*:*x*is an odd number} and
Set

*C*= {*x*:*x*is a multiple of 3}.
The
elements of the set (

*A*υ*C*)’ ∩*B*are

*Solution:*
ξ
= {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}

*A*= {4, 11, 13, 16}

*B*= {5, 7, 9, 11, 13, 15}

*C*= {6, 9, 12, 15}

(

*A*υ*C*)’ = {5, 6, 7, 8, 10, 14}
Therefore

**(***A***υ***C*)’ ∩*B*= {5, 7}.