If there are 6 elements in (A U B) and 1 Element in (A N B) answer the following:
A. What is the maximum number of elements possible for A?
B. What is the least possible number of elements in B?
c. if A has "n" elements, how many elements are in B?
To answer the given questions, let's break down the set operations and their properties.
A U B represents the union of sets A and B, which is the combination of all elements existing in either set. (A U B) will contain all elements from both A and B, without any repetitions.
A N B represents the intersection of sets A and B, which includes the elements that are common to both sets.
Now, let's address each question:
A. What is the maximum number of elements possible for A?
Since (A U B) contains 6 elements and (A N B) contains 1 element, we can deduce that the remaining 5 elements in (A U B) are unique to either A or B, but not in their intersection. Therefore, the maximum number of elements for A is 5.
B. What is the least possible number of elements in B?
Considering that (A N B) must have at least 1 element and (A U B) has a total of 6 elements, the minimum number of elements in B would be 6 - 1 = 5.
C. If A has "n" elements, how many elements are in B?
Since (A U B) contains 6 elements and (A N B) contains 1 element, we can calculate the number of elements in B by subtracting the number of elements in the intersection from the total number of elements in (A U B). Therefore, the number of elements in B would be (n + 1) if A has "n" elements.