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

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

Question 6 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
According to inclusion-exclusion principle, a n-tuple wise intersection is included if n is even.
A
True
B
False
Question 6 Explanation: 
According to inclusion-exclusion principle, a n-tuple wise intersection is included if n is odd and excluded if n is even.

Question 7 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
With reference to the given Venn diagram, what is the formula for computing?
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|
Question 7 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.

Question 8 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
Which of the following statement is incorrect with respect to generalizing the solution using the inclusion-exclusion principle?
A
including cardinalities of sets
B
excluding cardinalities of pairwise intersections
C
excluding cardinalities of triple-wise intersections
D
excluding cardinalities of quadraple-wise intersections
Question 8 Explanation: 
According to inclusion-exclusion principle, an intersection is included if the intersecting elements are odd and excluded, if the intersecting elements are even. Hence triple-wise intersections should be included.

Question 9 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
Counting intersections can be done using the inclusion-exclusion principle only if it is combined with De Morgan's laws of complementing.
A
true
B
false
Question 9 Explanation: 
The application of counting intersections can be fulfiled if and only if it is combined with De Morgan laws to count the cardinality of intersection of sets.

Question 10 [CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
Using the inclusion-exclusion principle, find the number of integers from a set of 1-100 that are not divisible by 2, 3 and 5.
A
22
B
25
C
26
D
33
Question 10 Explanation: 
Consider sample space S={1, ...100}. Consider three subsets A, B, C that have elements that are divisible by 2, 3, 5 respectively. Find integers that are divisible by A and B, B and C, A and C. Then find the integers that are divisible by A, B, C. Applying the inclusion-exclusion principle, 100 - (50 + 33 + 20) + (16 + 10 + 6) - 3 = 26.

There are 10 questions to complete.