Question

Define cardinal number of set.

a) The number of elements in a set.
b) The sum of elements in a set.
c) The average of elements in a set.
d) The product of elements in a set.

Fill in the gaps.
If n(A)=50,n(B)=40, and n(A−B)=20, then n(A∪B)= ______.
a) 30
b) 40
c) 50
d) 60

n(A)=n(A)−______.
a) n(B)
b) n(A∩B)
c) n( B)
d) n( A∪B)

n(U)=n(A∪B)+______.
a) n(A∩B)
b) n(A)
c) n(B)
d) n(A∩B)

Answer 1

The cardinal number of a set is the number of elements in that set. The union of sets A and B, given the cardinalities of A, B, and A minus B, is 60. When calculating the universe's total number of elements including A union B and their intersection, the result is 90.

Step-by-step explanation:

The cardinal number of a set is defined as the number of elements in a set. Considering the sets A and B, where n(A) represents the number of elements in set A and n(B) represents the number of elements in set B, we can use set operations to find the cardinality of their union and intersection.

If n(A) = 50, n(B) = 40, and n(A−B) = 20, then the number of elements in n(A∪ B), or the union of A and B, is calculated by n(A) + n(B) - n(A∩B). However, we do not have the value of n(A∩B) directly, but we can deduce it from the given information. Given that n(A−B) = 20, we can infer that n(A∩B) = n(A) - n(A−B), which gives us n(A∩B) = 50 - 20 = 30. Therefore, n(A∪ B) = 50 + 40 - 30 = 60.

For the next part of the question, n(A) = n(A) - n(A∩B) simplifies to n(A−B); thus, we have n(A) = 50 - 30 = 20, which is the number of elements in set A that are not in B.

Lastly, the total number n(U), or the universe of sets in question, is the sum of the union of sets A and B, and their intersection. So, n(U) = n(A∪ B) + n(A∩B). Filling in the known values, we get n(U) = 60 + 30 = 90.