1. Since Tom is the brother of Agatha, and Agatha is the mother of Raquel, it follows that Tom is the uncle of Raquel.

2. When a cook cannot recall the ingredients in a recipe, it is appropriate that she refresh her memory by consulting the recipe book. Similarly, when a student cannot recall the answers during a final exam, it is appropriate that she refresh her memory by consulting the textbook.

3. The Broadway Theater marquee says that The Phantom of the Opera is playing nightly. Therefore, it must be that case that Phantom is playing there tonight.

4. Since Christmas is always on a Thursday, it follows that the day after Christmas is always a Friday.

5. Suppose figure A is a triangle having two equal angles. It follows that figure A has two equal sides.

6. By accident Karen baked her brownies two hours longer than she should have. Therefore, they have probably been ruined.

7. After taking LSD, Alice said she saw a flying saucer land in the shopping center parking lot. Since Alice has a reputation for always telling the truth, we must conclude that a flying saucer really did land there.

8. Since Phyllis is the cousin of Denise, and Denise is the cousin of Harriet, it follows necessarily that Harriet is the cousin of Phyllis.

9. The picnic scheduled in the park for tomorrow will most likely be cancelled. It's been snowing for six days straight.

10. Circle A has exactly twice the diameter of circle B. From this we may conclude that circle A has exactly twice the area of circle B.

11. Robert has lost consistently at blackjack every day for the past several days. Therefore, it is very likely that he will win today.

12. Since John loves Nancy and Nancy loves Peter, it follows necessarily that John loves Peter.

13. This cash register drawer contains over 100 coins. Three coins selected at random were found to have dates earlier than 1960. Therefore, probably all of the coins in the drawer have dates earlier than 1960.

14. The Japanese attack on Pearl Harbor happened in either 1941 or 1951. But it didn't happen in 1941. Therefore, it happened in 1951.

15. Harry will never be able to solve that difficult problem in advanced calculus in the limited time allowed. He has never studied anything beyond algebra, and in that he earned only a C-.

16. Since x + y = 10, and x = 7, it follows that y = 4.

17. If acupuncture is hocus pocus, then acupuncture cannot relieve chronic pain. But acupuncture can relieve chronic pain. Therefore, acupuncture is not hocus pocus.

18. If inflation heats up, then interest rates will rise. If interest rates rise, then bond prices will decline. Therefore, if inflation heats up, then bond prices will decline.

19. Statistics reveal that 86 percent of those who receive flu shots do not get the flu. Jack received a flu shot one month ago. Therefore, he should be immune, even though the flu is going around now.

20. Since Michael is a Pisces, it necessarily follows that he was born in March.

Determine whether the following arguments are inductive or deductive. If an argument is inductive, determine whether it is strong or weak. If it is deductive, determine whether it is valid or invalid.