Some basic logic

Practise some important mathematical ideas.

Simply pick the answer you think is correct. You'll get immediate feedback. Whether you're right or not, you can keep choosing answers. When you're ready, move on to the next question.

Suppose that P => Q. Which of the following must then be true?
1. Not P => Not Q
2. Not Q => Not P
3. P <= Q
4. Q <= P
5. P implies Q
6. Q implies P
7. P is implied by Q
8. Q is implied by P
9. P is equivalent to Q
10. Not P implies Not Q
11. Not Q implies Not P
12. Not P is implied by Not Q
13. Not Q is implied by Not P
14. P is necessary for Q
15. Q is necessary for P
16. P is sufficient for Q
17. Q is sufficient for P
18. If P then Q
19. If Q then P
20. P if Q
21. Q if P
22. P only if Q
23. Q only if P
What is the negation of the statement P => Q?
1. Q => P
2. Q implies P
3. P and Not Q
4. P => Not Q
5. Not P => Not Q
What is the contrapositive of the statement P => Q?
1. P and Not Q
2. Not Q => Not P
3. Not P => Not Q
4. P => Not Q
5. Not P => Q
What is the negation of the statement "All cats are furry"?
1. All cats are not furry.
2. All cats are furry.
3. There is a cat that is furry.
4. There is a cat that is not furry.
What is the negation of the statement "There is a purple sheep"?
1. All sheep are not purple.
2. There is a sheep that is not purple.
3. All sheep are purple.
4. There is a purple sheep.
What is the negation of the statement "For every number n, there is some number m with m > n"?
1. For every number n, there is some number m with m ≤ n.
2. For every number n, every number m has m ≤ n.
3. There is some number n such that there is some number m with m ≤ n.
4. There is some number n such that every number m has m ≤ n.
What is the negation of the statement "There is a prime number p so that every prime number q satisfies q ≤ p"?
1. There is a prime number p so that every prime number q satisfies q > p.
2. There is a prime number p so that there is a prime number q with q > p.
3. For every prime number p, every prime number q satisfies q > p.
4. For every prime number p, there is a prime number q with q > p.