Page 149 - Mathematics_Form_Two

Sets
4. Which of the following sets are finite, because all elements of A belong to B. If A
infinite or empty:
=
(a) A {African countries in
Asian continent}
(b) B = {All the letters of the
English alphabets}
FOR ONLINE READING ONLY
=
(c) D {All months with 32 days}
(d) E = {2, 4, 6, 8, 10}
(e) F = {x : x > 20}
(f) G = {1, 2, 3, 4, 5, ...}
5. Give three examples of finite,
infinite, and empty sets in real life
situations.
6. Show that the set of letters needed
to spell "CATARACT" and the set
of letters needed to spell "TRACT"
are equal.
7. Which of the following sets are
empty?
A { := x x −A { := x x − 5 0 and is rational}= ,5 0 and is rational}= ,
22
B { : is an even prime number}= x x
C ={x :6< x <7, x ∈ !}
8. Find the pairs of equal sets from the
following sets, if any:
A {0},=
B = { >7 and < 4},x x
C { := x x − 5 0},=
2
D { := x x= 4},
E = {x : x is a positive integer
which is a root of the equation
E { : is a positive integer which is a root of the equation = x x x − 2 2x − 15 0},= {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1,
F = {x : x is the letter of the word
REAP}
Subsets
Set A is a subset of another set B if all
elements of A are also elements of B.
}
For example, if A = {a, b, c, e and
}
B = {a, b, c, d, e then A is a subset of B
143
Student's Book Form Two
MATHEMATIC F2 v5.indd 143
MATHEMATIC F2 v5.indd 143
has less elements than B, then A is called a
proper subset of B, denoted by A ⊂ B. If A
is a subset of B and the two sets are equal,
then A is called an improper subset of B,
written as A ⊆ B. If A = B, then A ⊆ B
and A ⊆ B .
Therefore, a subset of a set can either be
proper or improper.
Note: The empty set is a subset of any Mathematics for Secondary Schools
set, and a set is a subset of itself.
Example 7�5
List all the subsets of A = {a, b}.
Solution
The subsets of A = {a, b} are all
possible sets which can be obtained by
xx taking some or all elements of A.
Therefore, the subsets of set A are: { },
{a}, {b}, {a, b}.
Example 7�6
What are the subsets of B = {1, 2, 3}?
Solution {1, 2, 3 are all
}
The subsets of B =
possible sets which can be obtained by
taking some or all elements of set B.
Therefore, the subsets of set B are: { },
2, 3}
The number of subsets of a given set can
be obtained by using a formula 2 , where
n
n is number of elements of the given set.
The formula is obtained by observing
the pattern in forming subsets of sets as
shown in the following table.
11/10/2024 20:13:14
11/10/2024 20:13:14