In the field of Combinatorics, it is a counting method used to compute the cardinality of the union set. According to basic Inclusion-Exclusion principle:
- For 2 finite sets and , which are subsets of Universal set, then and are disjoint sets.
Hence it can be said that,
- Similarily for 3 finite sets , and ,
Inclusion-Exclusion principle says that for any number of finite sets , Union of the sets is given by = Sum of sizes of all single sets – Sum of all 2-set intersections + Sum of all the 3-set intersections – Sum of all 4-set intersections .. + Sum of all the i-set intersections.
In general it can be said that,
- Computes the total number of elements that satisfy at least one of several properties.
- It prevents the problem of double counting.
As shown in the diagram, 3 finite sets A, B and C with their corresponding values are given. Compute .
The values of the corresponding regions, as can be noted from the diagram are –
By applying Inclusion-Exclusion principle,
To determine the number of derangements( or permutations) of n objects such that no object is in its original position (like Hat-check problem).
As an example we can consider the derangements of the number in the following cases:
For i = 1, the total number of derangements is 0.
For i = 2, the total number of derangements is 1. This is .
For i = 3, the total number of derangements is 2. These are and .
- Arden's Theorem and Challenging Applications | Set 2
- Theory of Computation | Applications of various Automata
- Benefits of writing GATE exam
- Compiler Design | Recursive Descent Parser
- Computer Network | Efficiency of Stop & Wait
- Computer Network | Collision-Free Protocols
- Digital Logic | Number of Boolean functions
- Digital Logic | Number of possible Functions
- Tips to prepare for GATE
- Program to calculate Double Integration
- Compiler Design | Single pass, Two pass, and Multi pass Compilers
- Computer Network | Classless Inter Domain Routing (CIDR)
- Functionality of Computer Network
- TOC | Construction of the machines to produce residue modulo ‘2’ of binary numbers
Applying the Inclusion-Exclusion principle to i general events and rearranging we get the formula,
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.