Question

in a class of 120 students , 80 students study mathematics, 45 study history and 30 students study both the subjects. find the number of students who study niether mathematics nor history.

Answer 1

Using the principle of inclusion-exclusion, the number of students who study neither mathematics nor history in a class of 120 students is 25.

Step-by-step explanation:

To find the number of students who study neither mathematics nor history in a class of 120 students, we use the principle of inclusion-exclusion. The principle tells us that to find the total number of students studying either Mathematics or History, we add the number of students studying Mathematics to the number of students studying History, and subtract the number of students studying both.

So, we calculate it as follows:

• Number of students studying Mathematics (M) = 80
• Number of students studying History (H) = 45
• Number of students studying both Mathematics and History (both M and H) = 30

Total number of students studying either Mathematics or History (M or H) = M + H - (both M and H)

Total number of students studying either Mathematics or History (M or H) = 80 + 45 - 30 = 95

Now, to find the number of students studying neither Mathematics nor History, we subtract the number of students studying either subject from the total number of students:

Number of students studying neither Mathematics nor History = Total number of students - Number of students studying either Mathematics or History

Number of students studying neither Mathematics nor History = 120 - 95 = 25