Respuesta :
Answer: Â The required answers are
(a) 69,  (b) 21,  (c) 21  and  (d) 0.
Step-by-step explanation: Â We are given that the set A has 48 elements and the set B has 21 elements.
(a) To determine the maximum possible number of elements in A ∪ B.
If the sets A and B are disjoint, that is they do not have any common element. Then, A ∩ B = { }  ⇒  n(A ∩ B) = 0.
From set theory, we have
[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)=48+21-0=69.[/tex]
So, the maximum possible number of elements in  A ∪ B is 69.
(b) To determine the minimum possible number of elements in A ∪ B.
If the set B is a subset of set A, that is all the elements of set B are present in set A. Then,  n(A ∩ B) = 21.
From set theory, we have
[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)=48+21-21=48.[/tex]
So, the minimum possible number of elements in  A ∪ B is 21.
(c) To determine the maximum possible number of elements in A ∩ B.
If the set B is a subset of set A, that is all the elements of set B are present in set A. Then, n(A ∩ B) = 21.
So, the maximum possible number of elements in  A ∩ B is 21.
(d) To determine the minimum possible number of elements in A ∩ B.
If the sets A and B are disjoint, that is there is no common element in the sets A and B . Then,  n(A ∩ B) = 0.
So, the maximum possible number of elements in  A ∩ B is 0.
Thus, the required answers are
(a) 69,  (b) 21,  (c) 21  and  (d) 0.
