Use the Venn diagram below to find the number of elements in the region.
-n(C' )
A)29
B)14
C)24
D)39

Question

Use the Venn diagram below to find the number of elements in the region. 
-n(C' )
A)29 
B)14 
C)24 
D)39

Quizplus · Accepted Answer

From the Venn diagram, we know that n(A) = 30, n(C) = 40, and n(A ∩ C) = 16.

n(C') refers to the elements that are not in set C. We can find n(C') by subtracting n(C) from the total number of elements in the universe, which is 50. Therefore, n(C') = 50 - 40 = 10.

To find the number of elements in the region shaded in red, which is A' ∩ C', we need to subtract the number of elements in A ∩ C from the total number of elements that are not in set A or C.

n(A') refers to the elements that are not in set A. We can find n(A') by subtracting n(A) from the total number of elements in the universe, which is 50. Therefore, n(A') = 50 - 30 = 20.

n(A' ∪ C') refers to the total number of elements that are not in set A or C. We can find this by adding the number of elements in A' and C' and subtracting the number of elements in A ∩ C.

n(A' ∪ C') = n(A') + n(C') - n(A ∩ C) 
= 20 + 10 - 16 
= 14

Therefore, the number of elements in the region shaded in red is 14. The answer is C)24.

Use the Venn Diagram Below to Find the Number of Elements