Question

A set A has 620 elements and another set B has 380 elements. If the union of the sets A and B has 950 elements, the number of common elements in A and B is equal to

• A. 50
• B. 100
• C. 75
• D. 60

Answer 1

The Correct Option is A

The formula for the union of two sets is: \[ |A \cup B| = |A| + |B| - |A \cap B| \] Substitute the known values: \[ 950 = 620 + 380 - |A \cap B| \] \[ 950 = 1000 - |A \cap B| \] \[ |A \cap B| = 1000 - 950 = 50 \] To find the number of common elements in two sets, use the formula for the union of sets and solve for the intersection.