Page 150 - Mathematics_Form_Two

Sets

Set Subsets Number of subsets
{ } { } 1 = 2 0

{1} { }, {1} 2 = 2 = 2
1
{2, 3} { }, {2}, {3}, {2,3} 4 = 2 × 2 = 2 2 3
FOR ONLINE READING ONLY
{ }, {1}, {2}, {3}, {1,2}, {1,3}, {2, 3}, {1, 2, 3} 8 = 2 × 2 × 2 = 2
{1, 2, 3}
Mathematics for Secondary Schools Therefore, the formula for finding the number of subsets of a set with n elements is 2 .
2
n
{1, 2, 3,
, n}
{1, 2,

,n} { }, {1}, {1, 2}, ,

n
sets A and B do not have any elements in
Example 7�7
What is the total number of subsets that
sets. Otherwise, they are joint sets.
can be formed from the set common. Therefore, A and B are disjoint
A = {1, 2, 3, 4}
Exercise 7�3
Solution 1. List all the subsets of each of the
Since n(A) = 4, then 2 = 2 = 16. following sets:
n
4
Therefore, set A has a total of 16 subsets. (a) A = {1}
(b) B = Ø

Universal set (c) C = {Tito, Juma}
A universal set is a set that contains the 2. Find the number of subsets of each of
elements of all sets under consideration. the following sets.
It is denoted by the symbol µ or ∪ . For (a) A = {2, 4, 6, 8}

instance, the set of integers contains all
elements of sets of prime members, odd (b) B = {a, b, c, d, e, f, g}
numbers, and whole numbers. In this (c) { }
context, the ste of integers is considered
to be the universal set that contains all of In questions 3 to 5, which set in each pair
these elements. is a proper subset of the other? Use the
symbol ⊂.

Disjoint sets 3. A = {a, b, c, d, e, f, g, h} and

Two or more sets are said to be disjoint if B = {d, e, f}
they do not have any common elements. 4. A = {2, 4} and D = {2, 4, 5}
For instance, if A is the set of all odd 5. A = {1, 2, 3, 4, . . .} and
numbers less than 20 and B is the set of
all even numbers less than 20, then the C = {2, 4, 6, 8, . . .}

144
Student's Book Form Two

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MATHEMATIC F2 v5.indd 144