Exercise G

Which of the following is possible? If it is possible, give an example. If it is not possible, explain why.

1. A valid argument that has one false premise and one true premise

2. A valid argument that has a false conclusion

3. A valid argument, the conclusion of which is a necessary falsehood

4. An invalid argument, the conclusion of which is a necessary truth

5. A necessary truth that is contingent

6. Two necessarily equivalent sentences, both of which are necessary truths

7. Two necessarily equivalent sentences, one of which is a necessary truth and one of which is contingent

8. Two necessarily equivalent sentences that together are jointly impossible

9. A jointly possible collection of sentences that contains a necessary falsehood

10. A jointly impossible set of sentences that contains a necessary truth