Question

Let A={1,2,3} B={2,3,4} C={1,3,5} D={2,3}. Find the cardinality of sum of all the sets.

(a) 6

(b) 5

(c) 4

(d) 7

This question was posed to me by my school teacher while I was bunking the class.

The origin of the question is Number Theory topic in portion Number Theory of Data Structures & Algorithms II

Answer 1

Correct option is (b) 5

Best explanation: First, include the cardinalities of all the sets. Then, exclude the cardinalities of even intersections. Then include the cardinalities of odd intersections. Hence, 3+3+3+2-2-2-2-1-2-1+1+2+1+1-1=5.