{"id":7915,"date":"2022-05-11T14:28:16","date_gmt":"2022-05-11T08:58:16","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=7915"},"modified":"2025-12-16T10:40:45","modified_gmt":"2025-12-16T05:10:45","slug":"what-is-the-principal-of-inclusion-and-exclusion","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-is-the-principal-of-inclusion-and-exclusion\/","title":{"rendered":"What is the principal of inclusion and Exclusion"},"content":{"rendered":"\n

Principle of inclusion and exclusion can be defined as- Let we have A and B are finite sets. Then A \u222aB and A \u2229B are finite and n(A \u222aB) = n(A) + n(B) \u2212n(A \u2229B)<\/p>\n\n\n\n

That is, we find the number of elements in A or B (or both) by first adding n(A) and n(B) (inclusion) and then Subtracting n(A \u2229B) (exclusion) since its elements were counted twice<\/p>\n\n\n\n

Here n(A) is  the cardinality of set<\/a> A, n(B) is the cardinality of set B and n(A\u22c2B) is the cardinality of (A\u22c2B).<\/p>\n\n\n\n

For three sets-<\/p>\n\n\n\n

n(A \u222aB \u222aC) = n(A) + n(B) + n(C) \u2212n(A \u2229B) \u2212n(A \u2229C) \u2212n(B \u2229C) + n(A \u2229B \u2229C)<\/p>\n\n\n\n

Example: <\/h2>\n\n\n\n

In college, 49 study Physics , 37 study English and 21 study Biology. If 9 n(P\u22c2E) = 9<\/p>\n\n\n\n

n(E\u22c2B) = 5<\/p>\n\n\n\n

n(P\u22c2B) = 4<\/p>\n\n\n\n

n(P\u22c2E\u22c2B) = 3<\/p>\n\n\n\n

therefore, by using the formula we get<\/p>\n\n\n\n

n(P\u22c3E\u22c3B) = n(P) + n(E) + n(B) \u2013 n(P\u22c2E) \u2013 n(E\u22c2B) \u2013 n(P\u22c2B) + n(P\u22c2E\u22c2B)<\/p>\n\n\n\n

= 49 + 37 + 21 \u2013 9 \u2013 5 \u2013 4 + 3<\/p>\n\n\n\n

= 92<\/p>\n\n\n\n

Hence, the number of students in the college is 92.<\/p>\n\n\n\n

of these students study Maths Physics and English, 5 study English and Biology, 4 study Physics and Biology and 3 study Physics, English and Biology, find the number of students in the college.<\/p>\n\n\n\n

Solution:
Suppose P represents the number of students who study Physics, E represents the number of students who study English and B represent the number of students who study Biology.<\/p>\n\n\n\n

As we know that-<\/p>\n\n\n\n

Number of students in the group = n(P\u22c3E\u22c3B)<\/p>\n\n\n\n

Here it is given that-  n(P) = 49, n(E) = 37, n(B) = 21<\/p>\n\n\n\n

Example: Find the number of students at a college choosing at least one of the subject from mathematics, physics and statistics.<\/strong><\/p>\n\n\n\n

The data is given as-<\/strong><\/p>\n\n\n\n

65 study maths, 45 study physics, 42 study statistics<\/strong><\/p>\n\n\n\n

20 study maths and physics, 25 study maths and statistics, 15 study physics and statistics and 8 study all the three subjects.<\/strong><\/p>\n\n\n\n

Sol.<\/p>\n\n\n\n

Here we need to find , where<\/p>\n\n\n\n

M maths, P = physics, S = statistics<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Hence, by using Inclusion-Exclusion principle-<\/p>\n\n\n\n

Which gives-<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Therefore, we find that 100 students study at least one of the three subjects.<\/p>\n\n\n\n

Interested in learning about similar topics? Here are a few hand-picked blogs for you!<\/strong><\/p>\n\n\n\n