Let's analyze the given statements and deduce the other true statements for each case.

(a) Given:

• If that is Reuben's favorite joke, then the river is overflowing.
• If the river is overflowing, then the group has eaten lunch.

We are asked which statement must also be true.

The logic here follows the pattern of a transitive implication (if A → B and B → C, then A → C). Therefore, we can deduce that:

• If Reuben's favorite joke is true, then the group has eaten lunch.

(b) Given:

• If the tires are old, then Deshaun knows how to dance.
• The tires are old.

Here, the statement directly tells us that the tires are old, so using the first part of the implication, we can conclude that:

• Deshaun knows how to dance.

(c) Given:

• If the mouse escaped from the cat, then Pablo is a doctor.

We are not given additional information about the mouse's escape. Therefore, no further logical deductions can be made from this alone.

Would you like me to further explain the reasoning or discuss other related questions?

Related Questions:

1. What is the principle behind transitive implications in logic?
2. Can you give more examples of conditional statements and how they work together?
3. What is the role of the converse in logical implications?
4. How do compound logical statements work when more than one condition is involved?
5. What are the limitations of logical deductions based on insufficient information?

Tip:

When dealing with conditional (if-then) statements, always remember that the conclusion of one statement can sometimes serve as the premise for another, allowing you to chain them together.