The logical expression \((P \Rightarrow R) \Rightarrow (Q \Rightarrow R)\) can be analyzed using truth tables or logical equivalence transformations.

1. **Breaking down the expression:**
   - \(P \Rightarrow R\) means "If \(P\) is true, then \(R\) is true."
   - \(Q \Rightarrow R\) means "If \(Q\) is true, then \(R\) is true."
   - The entire expression is a conditional statement: If \((P \Rightarrow R)\) is true, then \((Q \Rightarrow R)\) is true.

2. **Truth Table:**
   Let's construct a truth table for the two variables \(P\), \(Q\), and \(R\):

| \(P\) | \(Q\) | \(R\) | \(P \Rightarrow R\) | \(Q \Rightarrow R\) | \((P \Rightarrow R) \Rightarrow (Q \Rightarrow R)\) |
|:-----:|:-----:|:-----:|:-------------------:|:-------------------:|:--------------------------------------------:|
|   T   |   T   |   T   |         T           |         T           |                      T                      |
|   T   |   T   |   F   |         F           |         F           |                      T                      |
|   T   |   F   |   T   |         T           |         T           |                      T                      |
|   T   |   F   |   F   |         F           |         T           |                      T                      |
|   F   |   T   |   T   |         T           |         T           |                      T                      |
|   F   |   T   |   F   |         T           |         F           |                      F                      |
|   F   |   F   |   T   |         T           |         T           |                      T                      |
|   F   |   F   |   F   |         T           |         T           |                      T                      |

3. **Interpretation:**
   The expression \((P \Rightarrow R) \Rightarrow (Q \Rightarrow R)\) is generally **true**, except when \(P\) is false, \(Q\) is true, and \(R\) is false (the sixth row of the truth table).

Would you like further details on logical equivalence transformations?

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### Related Questions:
1. How can we represent this expression using logical equivalences?
2. What would happen if we negated the expression \((P \Rightarrow R) \Rightarrow (Q \Rightarrow R)\)?
3. How does the truth table change if \(P\) and \(Q\) represent compound statements?
4. Can we prove this implication using rules of inference in formal logic?
5. How does this expression relate to the concept of contraposition?

### Tip:
In logic, \((P \Rightarrow Q)\) is equivalent to \((\neg P \lor Q)\), which is often useful when simplifying complex logical expressions.

Understand how to analyze the logical implication (P ⇒ R) ⇒ (Q ⇒ R) using truth tables. This solution explores key concepts like propositional logic, implications, and logical equivalence. Suitable for students in Grades 11-12 or undergraduate-level logic courses.

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