Page 148 - Mathematics_Form_Two

Sets

Generally, if n(A) = n(B), then the sets A
x
and B are said to be equivalent. That is, Again, Q = { :xx∈ and 7 << 10 }
A  B.
{8, 9= } , thus (Q)n = 2.
Example 7�3 It follows that, (P)n = n (Q) = 2.

Show that A = {4, 6} and B = {goat, dog} Therefore, P ≡ Q.
FOR ONLINE READING ONLY
are equivalent.
Mathematics for Secondary Schools Solution 1. Which of the following sets are finite,
Exercise 7�2
Since n(A) = 2 and n(B) = 2, then,

A ≡
B.
infinite or empty?
Therefore, the sets A and B are equivalent.
A ={Nairobi, Dar es Salaam}
(a)
Equal sets
(c)
C ={x : x ∈ N; x > 0}
Two sets, A and B are said to be equal if (b) B ={2, 4, 6,  , 36}
they are equivalent and their members (d) D ={All goats in your class}
are exactly the same regardless of the (e) E ={All mango trees in the
arrangement or order. For example, if world}
A = {1, 2, 3, 4} and B = {3, 1, 4, 2}, (f) F ={x : x is a multiple of 3}
then A = B since all elements of A are (g) G ={x : x is a prime numbers}
elements of B and all elements of B are (h) H ={1, 3, 5, 7}
also elements of A.
(i) I ={ }

Note: All equal sets are equivalent but 2. Which of the following pairs of sets
not all equivalent sets are equal. are equivalent?
(a) A = {a, b, c} and
Example 7�4 B = {b, c, d}

2
If P { :P= x x − 9= 0} and (b) B = {Rufiji, Ruaha, Malagarasi}
x
Q = { :xx∈ and 7 << 10 } , show that and C = {Lion, Leopard}
P ≡ Q. (c) D = {a, b, c, d} and

E = {a, b, c}
Solution
3. Which of the following sets are
Given P { :P= x x − 9= 0} and equal?
2
Q = { :xx∈ and 7 << 10 } it follows (a) A ={a, b, c, d},
x
that, B = {d, a, b, c},
P ={x : x −9 = 0} C = {a, e, i, o, u}.
2
{ 3, 3= − } (b) H = {a, b, c, d, e},

2
Thus, only 3− and 3 satisfy x − 9= 0. I {d, c, b, a},
=
Hence, (P)n = 2. J = {a, e, b, c, d}.

142
Student's Book Form Two

11/10/2024 20:13:13
MATHEMATIC F2 v5.indd 142 11/10/2024 20:13:13
MATHEMATIC F2 v5.indd 142