The issue of inclusion and exclusion involves an important principle-inclusion and exclusion principle, also known as inclusion and exclusion principle. That is, when two counting parts have repeated inclusion, in order not to repeat counting, the repeated part should be excluded from their sum.

Exclusion principle: for n things, if different classification standards are adopted and classified according to property A and property B respectively, then the number of things with property A or property B = Na+NB-NAB.

Example 1: There are 48 students in one class. The head teacher asked at the class meeting, "Who finished the Chinese homework? Please raise your hand! " 37 people raised their hands. Ask again: "Who finished the math homework? Please raise your hand! " 42 people raised their hands. Finally, I asked, "Who hasn't finished their Chinese and math homework?" No one raised their hands. Ask the number of students in this class to finish Chinese and math homework.

Analysis and answer: 37 people have finished Chinese homework, 42 people have finished math homework, and 37+42 = 79 people, more than the whole class.

This is because the number of people who have completed Chinese and math homework is counted once when counting the number of people who have completed Chinese homework and once when counting the number of people who have completed math homework, so it is counted again. So there are: 79-48 = 3 1 students who have finished the Chinese and math homework of this class.

Example 2: There are 36 students in one class. In one test, 25 students answered the first question correctly, 23 students answered the second question correctly, and 65,438+05 students answered two questions correctly. How many students are required to answer both questions wrong?

Analysis and solution: It is known that 25 people answered the first question correctly, 15 people answered both questions correctly, and it can be concluded that only 25- 15 = 15 people answered the first question correctly. It is also known that 23 people answered the second question correctly. Add the number of people who only answered the first question to the number of people who answered the second question, and the number of people who answered at least one question correctly is 10+23 = 33. So 36-33 = 3 people answered both questions wrong.