ACTIVITY A group of 250 students were interviewed about their color preference. They were asked to choose among red, blue and yellow. The following results are Set Application.
 given below
 35 students choose Red and Blue 
27 students choose Blue and Yellow
 22 students choose Red and Yellow 
45 students choose Red, blue and Yellow
 41 students choose Yellow
 46 students choose Blue 
56 students choose Red
 Make a vean diagram and answer the following.
 1, How many students choose Red and Blue but not Yellow? 
2. How many students choose Yellow only 
3. How many students did not choose any of the calors

Let's solve this problem using a Venn diagram. We are dealing with three sets:

- Set \( R \) for students who chose **Red**
- Set \( B \) for students who chose **Blue**
- Set \( Y \) for students who chose **Yellow**

The given data includes:

- 35 students chose **Red** and **Blue**.
- 27 students chose **Blue** and **Yellow**.
- 22 students chose **Red** and **Yellow**.
- 45 students chose all three colors: **Red**, **Blue**, and **Yellow**.
- 41 students chose **Yellow**.
- 46 students chose **Blue**.
- 56 students chose **Red**.

### Step 1: Venn Diagram Setup
To set up a Venn diagram, we begin by filling out the most specific part: students who chose all three colors.

- **Red ∩ Blue ∩ Yellow** = 45 students

Next, we move to students who chose two colors without the third color.

- **Red ∩ Blue** but not Yellow = 35 − 45 = **(−10 not possible, so we keep this for later)**.
- **Blue ∩ Yellow** but not Red = 27 − 45 = **(−18 similar issues )**  



A group of 250 students were interviewed about their color preference. They were asked to choose among red, blue, and yellow. The following results are given below: 35 students chose Red and Blue, 27 students chose Blue and Yellow, 22 students chose Red and Yellow, 45 students chose Red, Blue, and Yellow, 41 students chose Yellow, 46 students chose Blue, and 56 students chose Red. Make a Venn diagram and answer the following: 1. How many students chose Red and Blue but not Yellow? 2. How many students chose Yellow only? 3. How many students did not choose any of the colors?

Solve a color preference problem involving 250 students using a Venn diagram. Learn how to calculate the number of students who chose Red, Blue, and Yellow using set theory and the inclusion-exclusion principle. Find out how many students chose specific color combinations, including Red and Blue but not Yellow, and Yellow only.

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