Question 1:

The Venn diagrams in the answer space shows sets X, Y and Z such that the universal set, $\xi =X\cup Y\cup Z$
On the diagrams in the answer space, shade

$\begin{array}{l}(a)\mathrm{X’}\cap Y,\\ (b)\left(X\cup \mathrm{Y’}\right)\cap Z\end{array}$
 

 Solution:

1. X’ ∩ Y means the intersection of the region outside X with the region Y.
   
2. • Find the region of (X ∪ Y’) first.
   • (X ∪ Y’) means the union of the region X and the region outside Y.
   • The region then intersects with region Z to give the result of  (X ∪ Y’) ∩ Z.
   

Question 2:

The Venn diagrams in the answer space shows sets P, Q and R such that the universal set,
On the diagrams in the answer space, shade

1. Q ∩ R,
2. (P’ ∩ R) ∪ Q.

Solution:

1. Q ∩ R means the intersection of the region Q and the region R.
   
2. • Find the region of (P’ ∩ R) first.
   • (P’ ∩ R) means the region that is outside P and is inside R.
   • The union of this region with region Q give the result of (P’ ∩ R) ∪ Q.
   
   

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 2ⁿ = 2² = 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 ∪ P. List all the subset of set P.

Solution:

Set P has 3 elements, so the number of subsets of set P is 2ⁿ = 2³ = 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 = {x : 30 ≤ x < 42, x is an integer} and set P = {x : x is a number such that the sum of it its two digits is an even number}.
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 ∪ 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∪C)' = {5, 6, 7, 8, 10, 14}
Therefore  (A∪C)’ ∩ B = {5, 7}

Question 5:

Diagram below shows a Venn diagram with the number of elements of set P, set Q and set R.

Solution:

Question 6:

If the number of participants who participate in only one quiz is 76, find the total number of the participants.

Solution:

Question 7:

If the number of students who join both the Life Guards Club and the Martial Arts Club is 8, find the number of students who join only two clubs.

Solution: