If n (U) = 16, n (A) = 7 and n (B) = 12, Find:
a) n (A')
b) n (B')
c) greatest n (A n B)
d) least n (AUB)
A=11
Answer this question
If n (u) = 16 n (A) = 7 and n (B)=12 then n (A') =
A11
To find the answers to these questions, we need to understand some basic concepts from set theory:
1. Complement: The complement of a set A, denoted as A', is the set of all elements in the universal set U that are not in A.
2. Intersection: The intersection of two sets A and B, denoted as A ∩ B, is the set of elements that are common to both A and B.
3. Union: The union of two sets A and B, denoted as A ∪ B, is the set of all elements that belong to either A or B, or both.
Now, let's solve each part of the question step by step:
a) To find n(A'), we need to count the number of elements in the complement of set A. Since the universal set U has 16 elements and set A has 7 elements, the complement of A, A', will have 16 - 7 = 9 elements. Therefore, n(A') = 9.
b) Similarly, to find n(B'), we need to count the number of elements in the complement of set B. Since the universal set U has 16 elements and set B has 12 elements, the complement of B, B', will have 16 - 12 = 4 elements. Therefore, n(B') = 4.
c) To find the greatest number of elements in the intersection of sets A and B, we need to determine how many elements are common to both sets. From the given information, n(A) = 7 and n(B) = 12. The intersection of sets A and B, denoted as A ∩ B, can have a maximum of 7 elements since that is the size of set A. Therefore, the greatest n(A ∩ B) = 7.
d) To find the least number of elements in the union of sets A and B, we need to determine how many elements are in either of the sets. From the given information, n(A) = 7 and n(B) = 12. The union of sets A and B, denoted as A ∪ B, can have a minimum of 12 elements since that is the size of set B. Therefore, the least n(A ∪ B) = 12.
Student
a) n(U) - n(B-A)
b) n(U) - n(A-B)
c) well, A∩B ⊆ A
d) n(B) since A⊂(AUB)