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The image presents a matching exercise where properties of inequalities need to be associated with their correct definitions. Here's the solution:

1. **Tricotomía (Trichotomy)**: The correct definition is \( a < b \), \( a = b \), or \( a > b \), which matches with option **b**.
2. **Transitividad (Transitivity)**: This means if \( a < b \) and \( b < c \), then \( a < c \), which matches with option **a**.
3. **De la suma (Sum property)**: This refers to \( A < B \) and adding a positive number preserves the inequality \( Ap < Bp \), matching with option **c**.
4. **De la multiplicación (Multiplication property)**: If \( x < y \), then multiplying both by a positive number \( z \) maintains the inequality \( xz < yz \), matching with option **d**.

Thus, the correct match is **1b 2a 3c 4d**. This corresponds to the second option in the list: **1b 2a 3d 4c**.

Would you like more details, or do you have any questions?

### Related Questions:
1. What is the difference between trichotomy and transitivity?
2. Can you explain why the sum property works for inequalities?
3. How does the multiplication property change for negative numbers?
4. What is the formal definition of each inequality property?
5. How can these properties be applied in solving inequalities?

### Tip:
When working with inequalities, always pay attention to whether you're multiplying or dividing by negative numbers, as it reverses the inequality sign.

Relacione la propiedad de las desigualdades con su correcta definición.

Match the properties of inequalities with their correct definitions. Learn about key properties like Trichotomy, Transitivity, Sum, and Multiplication properties. Suitable for high school students in Grades 9-12.

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