If A = {p, q, r} and B = {q, p, r}, then check whether A=B or not
Solution :
Given A = {p, q, r} and B = {q, p, r}.
In the above sets, every element of A is also an element of B. ∴ A ⊆ B.
Similarly every element of B is also in A. ∴b ⊆ A .
Then from the above two relations, we can say A=B.
Examples-8.
If A = {1, 2, 3, ….} and N is the set of natural numbers, then check whether A
and N are equal?
Solution :
The elements are same in both the sets. Therefore, A ⊆ N and N ⊆ A.
Therefore, both A and N are the set of Natural numbers. Therefore the sets A and N are
equal sets i.e. A = N.
Examples-9.
Consider the sets A = {p, q, r, s} and B = {1, 2, 3, 4}. Are they equal?
Solution :
A and B do not contain the same elements. So, A not equal to B.
Examples-10.
Let A be the set of prime numbers smaller than 6 and B be the set of prime
factors of 30. Check if A and B are equal.
Solution :
The set of prime numbers less than 6, A = { 2,3,5}
The prime factors of 30 are 2, 3 and 5. So, P = { 2,3,5}
Since the elements of A are the same as the elements of P and vice versa therefore, A and
P are equal. i.e A ⊆ B,B ⊆ A, A => B
Examples-11.
Show that the sets C and B are equal, where
C = {x : x is a letter in the word ‘ASSASSINATION’}
B = {x : x is a letter in the word STATION}
Solution :
Given that C = {x : x is a letter in the word ‘ASSASSINATION’}
The roster form of the set C = {C,S,I,N,T,O}, since elements in a set cannot be repeated.
Also given that B = {x : x is a letter in the word STATION}