Logic 1.4 Section 3 & 4

5. A valid argument may have a false premise and a false conclusion.

True

6. A valid argument may have a false premise and a true conclusion.

True

9. A strong argument may have false premises and a probably false conclusion.

True

1.Some arguments, while not completely valid, are almost valid.

False

10. A strong argument may have true premises and a probably false conclusion.

False

11. A cogent argument may have a probably false conclusion.

False

13. If an argument has true premises and a true conclusion, we know that it is a perfectly good argument.

False

14. A statement may legitimately be spoken of as ''valid'' or ''invalid.''

False

15. An argument may legitimately be spoken of as ''true'' or ''false.''

False

3. Invalid deductive arguments are basically the same as inductive arguments.

False

7. A sound argument may be invalid.

False

8. A sound argument may have a false conclusion.

False

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

If you assume the premises are true, then the conclusion follows necessarily. So the argument is both deductive and valid for the same reason. Deductive, Blank, Valid

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

Robert is probably a rotten player who will continue to lose as long as he plays this game. In any event, there is very little reason to think that he will win today. Inductive, Weak, Blank

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

The word "necessarily" suggests that this argument is deductive. However, if the premises are assumed true it does not follow necessarily that the conclusion is true. Deductive, Blank, Invalid

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

The word "necessarily" suggests that this argument should be interpreted as deductive. But the word "loves" is not a transitive relation. The fact that A loves B, and B loves C, does not imply that A loves C. Deductive, Blank, Invalid

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

This argument is a causal inference, from cause to effect. Thus, it is inductive. The likelihood that Jack is immune is 86%. Anything more than 50% is strong. Inductive, Strong, Blank

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

This argument is a disjunctive syllogism; hence it is deductive. If the premises are assumed true, the conclusion is necessarily true, so the argument is valid. But note that the second premise is false, so the argument is unsound. Deductive, Blank, Valid

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.

This argument is a generalization, hence it is inductive. But the sample is too small to support the conclusion. Inductive, Weak, Blank

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.

This argument is a hypothetical syllogism; hence deductive. If the premises are assumed true, the conclusion is necessarily true; thus, the argument is valid. Note that the premises and conclusion link together like a chain. Deductive, Blank, Valid

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

This argument is a hypothetical syllogism; hence, deductive. Deductive, Blank, Valid

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-.

This argument is a prediction; thus, it is inductive. If the premises are assumed true, the conclusion is probably true, so the argument is strong. Inductive, Strong, Blank

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

This is a causal inference, from cause to effect. Brownies are normally cooked for around 20 minutes. Cooking them for two hours and twenty minutes would be seven times as long as they should be cooked. They have certainly been ruined. Inductive, Strong, Blank

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

This is a prediction. People do not usually go on picnics after a six-day snowfall. Inductive, Strong, Blank

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.

This is an argument based on mathematics. Hence it is deductive. If Circle A has twice the diameter (therefore, twice the radius) of Circle B, it's area is four times that of Circle B. Deductive, Blank, Invalid

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.

This is an argument from analogy, which makes it inductive. However, if you assume the premise is true, it is not probable that the conclusion is true Inductive, Weak, Blank

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.

This is an argument from authority. Alice was probably hallucinating. Inductive, Weak, Blank

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

This is an argument from definition. By definition, Friday is the day after Thursday, so the argument is valid. However, the premise is false, so the argument is unsound. Deductive, Blank, Valid

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

This is an argument from definition; hence deductive. All of the astrological signs cover a part of two months. Thus, if the premise is assumed true, it is not necessarily the case that the conclusion is true. Hence, the argument is invalid. Deductive, Blank, Invalid

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

This is an argument from mathematics; hence, deductive. The correct value for y is 3, not 4; thus, the argument is invalid. Deductive, Blank, Invalid

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.

This is an argument from signs. You can usually trust what a theater marquee says about what is playing there. Inductive, Strong, Blank

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

To prove this, from the side between the two equal angles construct a perpendicular line through the other vertex. The resulting two right triangles are then congruent by the angle-angle-side theorem. Hence the hypotenuses of these two triangles are equal, which proves that the original triangle has two equal sides. Deductive, Blank, Valid

12. A cogent argument must be inductively strong.

True

2.Inductive arguments allow for varying degrees of strength and weakness.

True

4.If a deductive argument has true premises and a false conclusion, it is necessarily invalid.

True