Inclusion-Exclusion Principle Multiple choice Questions and Answers (MCQs)

 

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Inclusion-Exclusion Principle Multiple choice Questions and Answers (MCQs)

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Question 1
Which one of the following problem types does inclusion-exclusion principle belong to?
A
Numerical problems
B
Graph problems
C
String processing problems
D
Combinatorial problems
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Question 1 Explanation: 
Inclusion-Exclusion principle is a kind of combinatorial problem. It is a counting technique to obtain the number of elements present in sets( two, three, etc., ).

Question 2
Which of the following is a correct representation of inclusion-exclusion principle?
A
|A U B|=|A|+|B|-|A, B|
B
|A, B|=|A|+|B|-|A U B|
C
|A U B|=|A|+|B|+|A, B|
D
|A, B|=|A|+|B|+|A U B|
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Question 2 Explanation: 
The formula for computing the union of two sets according to inclusion-exclusion principle is |A U B|=|A|+|B|-|A, B| where |A, B| represents the intersection of the sets A and B.

Question 3
..... is one of the most useful principles of enumeration in combinationatorics and discrete probability.
A
Inclusion-exclusion principle
B
Quick search algorithm
C
Euclid's algorithm
D
Set theory
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Question 3 Explanation: 
Inclusion-exclusion principle serves as one of the most useful principles of enumeration in combinationatorics and discrete probability because it provides simple formula for generalizing results.

Question 4
Which of the following is not an application of inclusion-exclusion principle?
A
Counting intersections
B
Graph coloring
C
Matching of bipartite graphs
D
Maximum flow problem
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Question 4 Explanation: 
Counting intersections, Graph coloring and Matching of bipartite graphs are all examples of inclusion-exclusion principle whereas maximum flow problem is solved using Ford-Fulkerson algorithm.

Question 5
Who invented the concept of inclusion-exclusion principle?
A
Abraham de Moivre
B
Daniel Silva
C
J.J. Sylvester
D
Sieve
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Question 5 Explanation: 
The concept of inclusion- exclusion principle was initially invented by Abraham de Moivre in 1718 but it was published first by Daniel Silva in his paper in 1854.

There are 5 questions to complete.

 

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