Page 159 - Mathematics_Form_Two

Sets

The complement of the two sets A and B Example 7�22



are; A = 1, 2, 6, 7, 8  and B = 3, 5,7,8 .
If A and B are two sets with some common

But A B = 1,2,3,4,5,6 .  elements, represent each of the following
1,2,3,4,5,6
A
B =
(
  87,
B) =
A
Thus, A(  B) =   87, sets in a Venn diagram.
(a) A∪B
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The set (A ∪ B)′ is shown in the following (b) A∩B
Mathematics for Secondary Schools

Venn diagram.
Solution
(a) A∪B
Similarly, A¢ B ={7,8} . The set A′ B′∩
¢Ç
is shown in the following Venn diagram.

The shaded region represents A∪B.

1 (b) A∩B
3 2
5 4
6

From the two Venn diagrams, it follows
that (A  B) =  A  B .

Therefore, (A  B) = A  B .

Example 7�21 The shaded region represent A∩B.

Represent A ∩in a Venn diagram and Example 7�23
shade the required region.
If A and B are two sets such that
Solution
The set A ∩is represented in in the n(A∩B) = 4, n(A∪B) = 6, and n(A) = 4:
followingVenn diagram. (a) How many elements are there in B?

(b) Between A and B, which set is a
subset of the other?

Solution

Using a Venn diagram, the two sets can
be represented as follows:
n
Therefore, A ∩( )n µ = A. + (A ) ′
(A) n
153
Student's Book Form Two

MATHEMATIC F2 v5.indd 153 11/10/2024 20:13:29
MATHEMATIC F2 v5.indd 153
11/10/2024 20:13:29