Repulsion refers to the relationship between sets and sets, two sets A and B, if there are independent parts and overlapping parts, then we call the overlapping parts the intersection of A and B, denoted as A B, as shown in the figure. The outermost box contains the set A, B, and other parts M, which is called the complete set, and is denoted as I.
The repulsive extremum that we want to introduce in this article refers to the minimum value of the intersection of the given set, which has a specific formula, students only need to memorize the formula, and directly bring it into the solution when they encounter the corresponding problem type.
The formula for the two repulsion extremums is: (a b)min=a+b-i
The formula for the extremum of the three repulsions: (a b c) min = a + b + c - 2i
The formula for the four repulsion extremums is: (a b c d) min=a+b+c+d-3i
And so on ......
Example 1:
There are 48 students in a class, and each person has at least one of the two electrical appliances of air conditioner and computer at home, and it is known that there are 41 people with air conditioner and 34 people with computer at home, so how many students have two electrical appliances at home at the same time?
a.21 b.24 c.27 d.30
Answer] c. Find the minimum value of the intersection of the two, and use the formula of the two to reject the extreme value, 41 + 34-48 = 27 (people), the answer is c.
Example 2:
Xiao Ming, Xiao Gang and Xiao Hong took an English test together, and it was known that there were 100 questions in the test, and Xiao Ming got 68 questions right, Xiao Gang got 58 questions right, and Xiao Hong got 78 questions right. Q: How many questions are there that all three of them get right?
a.4 question b8 question c12 Question D16 questions.
Answer] a. Find the minimum value of the intersection of the three repulsions, the three sets correspond to the questions, and the whole set corresponds to a total of 100 questions, and directly use the formula of the extremum of the three repulsions, 68 + 58 + 78-2 100 = 4 (questions), so the answer is a.
Example 3:
The school organized interest group activities, and a total of 100 people signed up. Among them, 80 students signed up for the table tennis group, 72 students signed up for the badminton group, 65 students signed up for the volleyball team, and 98 students signed up for the basketball team. Q: How many people have signed up for each of the four interest groups?
a.5 people b10 people c15 people d20 people.
Answer] c. Find the minimum value of the intersection of the four repulsions, the four sets correspond to people, the whole set corresponds to a total of 100 people, directly use the formula of the extreme value of the four repulsions, 80 + 72 + 65 + 98-3 100 = 15 (people), the answer is c.
Through these examples, the common test question type that rejects extreme values has been shown to you, isn't it particularly simple?Hurry up and memorize the formula for repulsive extremums!