Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To find maximum value and minimum value in a set we have to use ven diagram from set theory.
Here we are taking an example?
Let A and B be 2 sets having elements 4 and 7 respectively. Then write the maximum number of elements that A∪B can have.
Let us assume that:
Number of elements of A is equal to n (A).
Number of elements of B is equal to n (B).
Number of elements of A∩B is equal to n (A∩B).
Now, the formula for the elements of A U B is as follows:
n(A∪B)=n(A)+n(B)−n(A∩B)
It is given in the question that, number of elements in set A is equal to 4 and number of elements in set B is equal to 7. So, we can write:
n (A) = 4, n (B) = 7
n (A∩B): the number of elements which are common in both the sets A and B.
We have to find the maximum number of elements which are in n(A∪B). So, the maximum of n(A∪B) is when n(A∩B) is minimum and the minimum of n(A∩B) is 0.
n(A∪B)=n(A)+n(B)−n(A∩B)⇒n(A∪B)=4+7−0⇒n(A∪B)=11
Hence, the maximum number of elements in A∪B is 11.
Note: You might be wondering, why for maximizing the n (A∪B) we have to minimize n (A∩B) and why the minimum value of n (A∩B) is 0.
In the formula for n (A∪B),
n(A∪B)=n(A)+n(B)−n(A∩B)
L.H.S will be maximized when in the R.H.S; the term after minus sign will be minimized. Hence, n (A∩B) must be minimized.
The minimum possible value of n (A∩B) is 0 means that the elements in the set A and B are such that there is not a single element is common in both the sets. And it could be possible that we have two sets and the sets have no element in common.
When no elements is common in both the sets, the n (A∩B) is ∅.
The set which has no element in it is called a null set or an empty set.
By this we can find maximum and minimum value in a set.
To know more about set here:
https://brainly.com/question/28860949
#SPJ4
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
