suppose  p-q is true and q-r is false then is p-r also false?

To answer whether \( p - r \) is false given that \( p - q \) is true and \( q - r \) is false, we need to examine what the notation means.

Assuming that the expressions represent **logical implications**:

- \( p - q \) means "if \( p \), then \( q \)" (i.e., \( p \implies q \)).
- \( q - r \) means "if \( q \), then \( r \)" (i.e., \( q \implies r \)).

### Given Information:
- \( p - q \) (or \( p \implies q \)) is **true**.
- \( q - r \) (or \( q \implies r \)) is **false**.

For \( q - r \) to be false, the only scenario where an implication is false is when the **premise is true** but the **conclusion is false**. So, we deduce:
- \( q \) is **true**.
- \( r \) is **false**.

Now, we use this information to check \( p - r \) (i.e., \( p \implies r \)).

Since \( r \) is false, for \( p - r \) to be true, \( p \) must also be false (because the only situation where an implication is false is when the premise is true and the conclusion is false).

### Conclusion:
- If \( p \) were true, then \( p \implies r \) would be false because \( r \) is false.
- Therefore, \( p - r \) is **false** in this case.

### Summary:
Yes, \( p - r \) is false given that \( p - q \) is true and \( q - r \) is false.

Would you like further details on logical implications or clarifications?

Here are 5 relative questions for further exploration:
1. What is the truth table for logical implications?
2. Can two false premises in a chain of implications lead to a true conclusion?
3. How does contrapositive reasoning work in logical implications?
4. What are common examples where implications are used in real-world scenarios?
5. Can we deduce anything else about \( p \) based on the given conditions?

**Tip:** Remember that a logical implication is false only when the premise is true and the conclusion is false.

suppose p-q is true and q-r is false then is p-r also false?

Explore the solution to the logical implication problem where p → q is true and q → r is false. This step-by-step solution explains the conditions for implications and evaluates whether p → r is also false. Suitable for students in Grades 10-12.

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