In a class of 42 student,25 offer biology,15 offer history and 18 do biology but not history
Solve
To determine the number of students who offer both biology and history, we need to use the principle of inclusion-exclusion.
Let's break down the given information:
- The number of students offering biology = 25
- The number of students offering history = 15
- The number of students offering biology but not history = 18
Now, let's use the principle of inclusion-exclusion to find the number of students offering both biology and history.
Step 1: Find the total number of students offering biology or history.
Total students offering biology = 25
Total students offering history = 15
Total students offering biology or history = Total students offering biology + Total students offering history - Total students offering both biology and history
Total students offering biology or history = 25 + 15 - Total students offering both biology and history
Step 2: Find the total number of students offering only biology.
Total students offering only biology = Total students offering biology - Total students offering both biology and history.
Total students offering only biology = 25 - 18 = 7
Step 3: Find the total number of students offering only history.
Total students offering only history = Total students offering history - Total students offering both biology and history.
Total students offering only history = 15 - 18 = -3
Step 4: Find the number of students offering both biology and history.
To find the number of students offering both biology and history, subtract the number of students offering only biology from the total students offering biology.
Students offering both biology and history = Total students offering biology - Total students offering only biology
Students offering both biology and history = 25 - 7 = 18
Therefore, the number of students offering both biology and history is 18.
To solve this problem, we can use the principles of set theory and visualize the information in a Venn diagram. Let's begin by representing the number of students who take Biology as "B," the number of students who take History as "H," and the number of students who take both Biology and History as "B ∩ H."
We know that:
- The total number of students in the class is 42.
- The number of students who take Biology is 25.
- The number of students who take History is 15.
- The number of students who take Biology but not History is 18.
Now, using these facts, we can find the number of students who take both Biology and History using the formula:
B + H - (B ∩ H) = Total number of students
Substituting the known values:
25 + 15 - (B ∩ H) = 42
Simplifying the equation, we have:
40 - (B ∩ H) = 42
Now, let's solve for (B ∩ H):
(B ∩ H) = 40 - 42
(B ∩ H) = -2
However, we cannot have a negative value representing the number of students taking both Biology and History, so there must be an error in the information provided.
To answer the question accurately, we need to revise the given numbers so that we have the correct relationship between the sets.