Use venn-diagram to check the validity of the following argument :
`S_(1)` : if a man is a bachelor, he is unhappy.
`S_(2)`: If a man is unhappy , he dies young .
S : All bachelors die young.

Explanation

To solve the problem using a Venn diagram, we will analyze the statements step by step.

### Step 1: Understand the Statements
1. **S1**: If a man is a bachelor, he is unhappy.
- This implies that all bachelors are included in the set of unhappy people.

2. **S2**: If a man is unhappy, he dies young.
- This implies that all unhappy people are included in the set of people who die young.

3. **S**: All bachelors die young.
- This is what we need to prove based on the previous statements.

### Step 2: Draw the Venn Diagram
1. **Draw three circles**:
- Let Circle A represent **Bachelors**.
- Let Circle B represent **Unhappy people**.
- Let Circle C represent **People who die young**.

2. **Place Circle A inside Circle B**:
- Since all bachelors are unhappy, Circle A (Bachelors) is a subset of Circle B (Unhappy people).

3. **Place Circle B inside Circle C**:
- Since all unhappy people die young, Circle B (Unhappy people) is a subset of Circle C (People who die young).

### Step 3: Analyze the Relationships
- From the Venn diagram:
- Since Circle A is inside Circle B, and Circle B is inside Circle C, this means that Circle A (Bachelors) is also inside Circle C (People who die young).

### Step 4: Conclusion
- Therefore, we conclude that all bachelors die young, which validates statement S.

### Final Answer
The argument is valid; all bachelors die young.

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