In a class of 55 students, 40 like Science and 29 like Mathematics. If each student likes at least one subject, answer the following questions.
How many like only Science?

Options

A. 29
B. 15
C. 26
D. 19

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the given information
We have:
- Total number of students (Universal Set, U) = 55
- Students who like Science (N(S)) = 40
- Students who like Mathematics (N(M)) = 29
- Each student likes at least one subject.

### Step 2: Use the formula for the union of two sets
The formula for the union of two sets is:
\[ N(S \cup M) = N(S) + N(M) - N(S \cap M) \]
Where:
- \( N(S \cup M) \) is the total number of students who like either Science or Mathematics.
- \( N(S \cap M) \) is the number of students who like both subjects.

### Step 3: Substitute the known values into the formula
Since all students like at least one subject, we can set \( N(S \cup M) = 55 \):
\[ 55 = 40 + 29 - N(S \cap M) \]

### Step 4: Solve for the intersection (students who like both subjects)
Rearranging the equation gives:
\[ N(S \cap M) = 40 + 29 - 55 \]
\[ N(S \cap M) = 69 - 55 \]
\[ N(S \cap M) = 14 \]
So, 14 students like both Science and Mathematics.

### Step 5: Find the number of students who like only Science
To find the number of students who like only Science, we use the formula:
\[ N(\text{only } S) = N(S) - N(S \cap M) \]
Substituting the known values:
\[ N(\text{only } S) = 40 - 14 \]
\[ N(\text{only } S) = 26 \]

### Final Answer
The number of students who like only Science is **26**.

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