Question

With reference to the given Venn diagram, what is the formula for computing |AUBUC| (where |x, y| represents intersection of sets x and y)?

(a) |A U B U C|=|A|+|B|+|C|-|A,B|-|A,C|-|B,C|+|A, B,C|

(b) |A, B,C|=|A|+|B|+|C|-|A U B|-|A U C|-|B U C|+|A U B U C|

(c) |A, B,C|=|A|+|B|+|C|+|A,B|-|A,C|+|B,C|+|A U B U C|

(d) |A U B U C|=|A|+|B|+|C| + |A,B| + |A,C| + |B,C|+|A, B,C|

I have been asked this question at a job interview.

Query is from Number Theory in section Number Theory of Data Structures & Algorithms II

Answer 1

Right answer is (a) |A U B U C|=|A|+|B|+|C|-|A,B|-|A,C|-|B,C|+|A, B,C|

Best explanation: The formula for computing the union of three sets using inclusion-exclusion principle is|A U B U C|=|A|+|B|+|C|-|A,B|-|A,C|-|B,C|+|A, B,C|  where |A,B|, |B,C|, |A,C|, |A,B,C| represents the intersection of the sets A and B, B and C, A and C, A, B and C respectively.