Give the numbers of elements in the region marked IV in the figure. $$| U | = 1,100 , | A | = 650 , | B | = 400 , | A \cap B | = 75$$
A) 125 elements
B) 400 elements
C) 0 elements
D) 325 elements
E) 575 elements

Question

Give the numbers of elements in the region marked IV in the figure. $$| U | = 1,100 , | A | = 650 , | B | = 400 , | A \cap B | = 75$$ 
A) 125 elements 
B) 400 elements 
C) 0 elements 
D) 325 elements 
E) 575 elements

Quizplus · Accepted Answer

To find the number of elements in region IV, we need to subtract the number of elements in regions I, II, and III from the total number of elements in U.

Region I: Elements only in A (total A - overlap with B) 
= |A| - |A∩B| = 650 - 75 = 575

Region II: Elements only in B (total B - overlap with A) 
= |B| - |A∩B| = 400 - 75 = 325

Region III: Elements in both A and B (total overlap) 
= |A∩B| = 75

Therefore, the number of elements in region IV is:
|U| - |A| - |B| + |A∩B| = 1100 - 650 - 400 + 75 = 125

The correct answer is (D) 325 elements.

Give the Numbers of Elements in the Region Marked IV ∣U∣=1,100,∣A∣=650,∣B∣=400,∣A∩B∣=75| U | = 1,100 , | A | = 650 , | B | = 400 , | A \cap B | = 75∣U∣=1,100,∣A∣=650,∣B∣=400,∣A∩B∣=75

Give the Numbers of Elements in the Region Marked IV $| U | = 1,100 , | A | = 650 , | B | = 400 , | A \cap B | = 75$