## Second Set of Practice Exercises onNecessary Conditions and Sufficient Conditions

Examples: In each of the following three pairs of statements, the first member of the pair is a sufficient condition for the second.

1. being a boy
2. being a male

Being a boy is a sufficient condition for being a male, i.e. being a boy guarantees (/ensures) that one is a male.

3. unscrewing a light bulb
4. the bulb's being unlit

5. being a legal resident of Canada, more than 30 years old, having a gross income in excess of \$22,000
6. being required to file a Canadian Income Tax return
Note: a is a logically sufficient condition for b.
Note: c is a physically sufficient condition for d.
Note: e is a legally sufficient condition for f.

For each of the following pairs, say whether the first is a logically necessary condition (LNC) for the second, whether it is a logically sufficient condition (LSC), whether both a logically necessary and a logically sufficient condition (LNC & LSC), or whether it is neither (X). For the answers, click on "Answers" at the bottom of this page (after question #27).
1. (a) x is blue.
(b) x is colored.

2. (a) x has a smell.
(b) x smells like tuna.

3. (a) Bob drew the eight of Spades from an ordinary deck of playing cards.
(b) Bob drew a black card from a deck of ordinary playing cards.

4. (a) Today is Wednesday.
(b) It is now later than Tuesday and earlier than Thursday.

5. (a) Alice has a brother-in-law.
(b) Alice is not an only child.

6. (a) Alice's daughter is married.
(b) Alice is a parent.

7. (a) Alice's daughter is married.
(b) Alice is a grandmother.

8. (a) Alice has four apples and three bananas.
(b) Alice has some fruit.

9. (a) Alice has some poultry.
(b) Alice has two chickens and four turkeys.

10. (a) Alice loves candies.
(b) Alice loves all sweet foods.

11. (a) Mike owns a car.
(b) There is a car that is owned by Mike.

12. (a) Mike is driving a car.
(b) Mike owns a car.

13. (a) Mike wants a new bike.
(b) There is a new bike (i.e. a new bike exists).

14. (a) Mike is riding a new bike.
(b) There is a new bike (i.e. a new bike exists).

15. (a) Everybody loves somebody (or other).
(b) There is some (one) person who is loved by everyone.

16. (a) All women pay taxes.
(b) Anyone who does not pay taxes is not a woman.

17. (a) Some women pay taxes.
(b) Some taxpayers are women.

18. (a) All women pay taxes.
(b) All taxpayers are women.

19. (a) Pianos are stringed instruments.
(b) Pianos and violins are stringed instruments.

20. (a) It is Tuesday or Wednesday.
(b) It is Tuesday.

21. (a) John loves Mary.
(b) Mary loves John.

22. (a) Terry is Leslie's brother.
(b) Leslie is Terry's brother.

23. (a) Sally is vacuum cleaning a chair.
(b) A chair exists.

24. (a) Sally is thinking about Snow White.
(b) Snow White exists.

25. (a) Water contracts when it freezes.
(b) Not all substances expand when they freeze.

26. (a) There are two apples and two oranges in Sue's basket.
(b) There are fewer than six pieces of fruit in Sue's basket.

27. (a) There are two apples and two oranges in Sue's basket.
(b) Sue has more than three pieces of fruit.