1. Which of the following is a valid argument? You answered:

All of the students on the Dean's List have a GPA of 3.5 or better. Some English majors are on the Dean's List, so some English majors must not have have a GPA of 3.5 or better.

Checking the three rules:

1. 1. Negative conclusion, negative premise. The conclusion is negative ("majors must not have"), but neither of the premises are, so this argument violates the rule and is therefore not valid.

1. Which of the following is a valid argument? You answered:

My company is laying off some of its best workers. I don't work for a good company. Therefore, a good company doesn't lay off some of its best workers.

Begin by restating the argument using state-of-being verbs:

Company is downsizer. My company is not good company. Therefore, good company is not downsizer.

1. Negative conclusion, negative premise. The conclusion is negative ("is not downsizer"), and so is one premise ("is not good"), so this argument satisfies the first rule.
2. Distributed terms in the conclusion, distributed in the premises. In a claim of the pattern "No A is B," both A and B are distributed, so here "good company" and "downsizer" are distributed in the conclusion. "Good company" is distributed in the second premise, but "downsizer" is not distributed in the first, so the argument does not satisfy the second rule, and is invalid.

2. Which rule does the following syllogism violate? "Some stocks are not good investments. I want a good investment for my retirement fund. Therefore, I don't want stocks for my retirement fund." You answered:

Even or odd number of negatives in conclusion and premises.

Always begin by restating the claims with state-of-being verbs: "Some stocks are not good. All that is wanted is good. Therefore, no stocks are wanted." The problem here may have been that second premise. How do you know that "I want a good investment for my retirement fund" is equivalent to "All that is wanted is good"? The first question to ask is, "Does this mean that there are some good investments I don't want, or some investments I want that aren't good." Obviously, the latter is not what is meant by the second premise.

Now that you have the claims clearer in mind, apply the rule of even or odd negatives. The conclusion is negative ("don't want"), and so is one of the premises ("not good"), so the argument satisfies this rule. Try again!

2. Which rule does the following syllogism violate? "Some stocks are not good investments. I want a good investment for my retirement fund. Therefore, I don't want stocks for my retirement fund." You answered:

Middle term distributed.

Always begin by restating the claims with state-of-being verbs: "Some stocks are not good. All that is wanted is good. Therefore, no stocks are wanted." The problem here may have been that second premise. How do you know that "I want a good investment for my retirement fund" is equivalent to "All that is wanted is good"? The first question to ask is, "Does this mean that there are some good investments I don't want, or some investments I want that aren't good." Obviously, the latter is not what is meant by the second premise.

Now that you have the claims clearer in mind, apply the rule of middle-term distribution. "Good" is the middle term, and it is distributed in the first premise, so the argument does not violate this rule. Try again!

2. Which rule does the following syllogism violate? "Some stocks are not good investments. I want a good investment for my retirement fund. Therefore, I don't want stocks for my retirement fund." You answered:

None of the above: the argument is valid.

Always begin by restating the claims with state-of-being verbs: "Some stocks are not good. All that is wanted is good. Therefore, no stocks are wanted." The problem here may have been that second premise. How do you know that "I want a good investment for my retirement fund" is equivalent to "All that is wanted is good"? The first question to ask is, "Does this mean that there are some good investments I don't want, or some investments I want that aren't good." Obviously, the latter is not what is meant by the second premise. Now that you have the claims clearer in mind, try again.

3. Which rule does the following argument violate? "Some American-made products are the of the finest quality. We only buy finest quality products. Therefore, we only buy American-made products." You answered:

Even or odd number of negatives in conclusion and premises.

Always begin by restating the claims with state-of-being verbs: "Some American-made are finest. All bought are finest. All bought are American-made." One problem here may have been the "only" in the second premise and the conclusion. How do you know that "We only buy the finest quality products" is equivalent to "All bought are finest"? The first question to ask is, "Does this mean that some things we buy are not the finest products, or that there are some finest products we don't buy"? Obviously, the former is not what is meant by the second premise.

Now that you have the claims clearer in mind, apply the first rule. The conclusion is not negative, nor is either of the premises, so the argument satisfies this rule. Try again!

3. Which rule does the following argument violate? "Some American-made products are the of the finest quality. We only buy finest quality products. Therefore, we only buy American-made products." You answered:

Distributed terms in the conclusion are distributed in the premises.

Always begin by restating the claims with state-of-being verbs: "Some American-made are finest. All bought are finest. All bought are American-made." One problem here may have been the "only" in the second premise and the conclusion. How do you know that "We only buy the finest quality products" is equivalent to "All bought are finest"? The first question to ask is, "Does this mean that some things we buy are not the finest products, or that there are some finest products we don't buy"? Obviously, the former is not what is meant by the second premise.

Now that you have the claims clearer in mind, apply the second rule. The only distributed term in the conclusion is "bought," and it is also distributed in the second premise, so the argument satisfies this rule. Try again!

3. Which rule does the following argument violate? "Some American-made products are the of the finest quality. We only buy finest quality products. Therefore, we only buy American-made products." You answered:

None of the above: the argument is valid.

Always begin by restating the claims with state-of-being verbs: "Some American-made are finest. All bought are finest. All bought are American-made." One problem here may have been the "only" in the second premise and the conclusion. How do you know that "We only buy the finest quality products" is equivalent to "All bought are finest"? The first question to ask is, "Does this mean that some things we buy are not the finest products, or that there are some finest products we don't buy"? Obviously, the former is not what is meant by the second premise. Now that the premises are clearer in your mind, try again, because this argument is not valid.

Congratulations!

You have completed the exercises on non-universal syllogisms. You may now continue with related sections on:

[Conditionals] [Universal Syllogisms]

[Further Deductive Exercises] [Exit Quit for Syllogisms]

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