https://file.aiquickdraw.com/mathbot/file/1727455798215136pc2c4.jpg

In this question, we have a chain of conditional statements that can be solved using logic, particularly the **Law of Syllogism** (also known as transitive property in logic).

Let's break it down:

- **Statement 1**: If Jane cleans her room, then her mother will be happy.
- **Statement 2**: If Jane's mother is happy, then Jane will get ice cream.
- **Statement 3**: Jane cleaned her room.

Using **Statement 3**, we know Jane cleaned her room, so according to **Statement 1**, her mother will be happy. Then, using **Statement 2**, if her mother is happy, Jane will get ice cream.

### Conclusion:
Jane will get ice cream.

### Law:
Law of Syllogism.

Would you like any further explanation on the steps? Here are 5 related questions:

1. What is the Law of Syllogism in logic?
2. Can the Law of Syllogism be used with more than two statements?
3. How does the Law of Syllogism differ from the Law of Detachment?
4. What happens if one of the premises in a syllogism is false?
5. Can you apply this logic to everyday decision-making?

**Tip**: The Law of Syllogism works by connecting two conditional statements where the conclusion of one is the hypothesis of the next.

If little Jane cleans her room, then her mother will be happy. If Jane's mother is happy, then Jane will get ice cream. Jane cleaned her room.

Learn how to draw logical conclusions using conditional statements with the example of Jane cleaning her room. This problem uses the Law of Syllogism, demonstrating how conclusions are formed when premises are connected.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation