Indicate whether each of the following sentences is true. For those that are true, explain why they are true. For those that are false, show why they are false by giving a counterexample.
1. Every argument with a false conclusion is invalid.
2. Every argument with a false premise is invalid.
3. Every argument with a false premise and a false conclusion is invalid.
4. Every argument with a false premise and a true conclusion is invalid.
5. Every argument with true premises and a false conclusion is invalid.
6. Every argument with a true conclusion is sound.
7. Every argument with a false conclusion is unsound.