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Sagot :
The ven diagram from set theory must be used to determine the highest value and minimum value in a set.
We're using this as an illustration.
Let A and B represent two sets with 4 and 7 items, respectively. The maximum number of elements that A and B can have is then written.
So let's assume:
A's element count is equal to n. (A).
B's element count is equal to n. (B).
The sum of the elements of A and B is n (A and B).
Now, here is the equation for the components of A U B:
n(A∪B)=n(A)+n(B)−n(A∩B)
The answer to the question states that set A's element count is four, whereas set B's element count is seven. We can thus write:
The number of elements that are included in both sets A and B is represented by the numbers n (A) = 4 and n (B) = 7.
The maximum number of elements in n(A,B) must be determined. Therefore, when n(AB) is smallest and when n(AB) is zero, n(AB) is at its maximum.
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.
You might be asking why n (AB) must be minimized in order to be maximized, and why the minimal value of n (AB) 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 fact that n (AB) can take on any value less than 0 indicates that there are no elements in sets A or B that are shared by both sets. Furthermore, it's possible that the two sets we have don't share any elements.
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 value in a set.
To know more about set here:
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