CCAT Syllogisms and Deductions 2 — Questions and Answers
Question 1: Premises: All athletes are disciplined. All disciplined people are successful. Conclusion: All athletes are successful. Is the conclusion valid?
- Valid (Correct answer)
- Invalid
- Possibly valid
- Cannot determine
Correct answer: Valid
Valid syllogism: All A are B; All B are C; therefore All A are C. Athletes (A) are disciplined (B) are successful (C).
This is a valid categorical syllogism: All A are B; All B are C; therefore All A are C. Athletes are a subset of disciplined people, which is a subset of successful people. Athletes are therefore successful.
Question 2: Premises: No fish are mammals. All whales are mammals. Conclusion: No whales are fish. Is this valid?
- Valid (Correct answer)
- Invalid
- Possibly valid
- Cannot determine
Correct answer: Valid
Fish and mammals are disjoint. Whales are all mammals. Since no mammal is a fish, no whale is a fish. Valid.
Fish and mammals are disjoint sets. Whales are a subset of mammals. Since no mammal is a fish, and all whales are mammals, no whale is a fish. The conclusion is valid.
Question 3: Premises: Some teachers are authors. All authors are creative. Conclusion: Some teachers are creative. Is this valid?
- Valid (Correct answer)
- Invalid
- Possibly valid
- Cannot determine
Correct answer: Valid
Some teachers are authors, and all authors are creative. Those teachers who are authors must be creative.
Some teachers are in the author set. All members of the author set are creative. Therefore those teachers (who are authors) are creative. 'Some teachers are creative' follows necessarily.
Question 4: Premises: All birds have feathers. This animal has feathers. Conclusion: This animal is a bird. Is this valid?
- Valid
- Invalid — affirming the consequent (Correct answer)
- Valid only if the animal is small
- Cannot determine
Correct answer: Invalid — affirming the consequent
This commits the fallacy of affirming the consequent. Having feathers does not mean it's a bird — the premise says all birds have feathers, not that all feathered things are birds.
The valid inference is: bird implies feathers. But having feathers does not imply being a bird. This is the fallacy of affirming the consequent: P implies Q; Q; therefore P — invalid.
Question 5: Premises: No vegetarians eat meat. Sarah eats meat. Conclusion: Sarah is not a vegetarian. Is this valid?
- Valid (Correct answer)
- Invalid
- Possibly valid
- Cannot determine
Correct answer: Valid
Contrapositive: if someone eats meat, they are not a vegetarian. Sarah eats meat, so Sarah is not a vegetarian. Valid.
No vegetarians eat meat means: vegetarians and meat-eaters are disjoint. Sarah eats meat, so Sarah is a meat-eater, and therefore not a vegetarian. The conclusion is valid.
Question 6: Premises: All politicians make promises. Some promise-makers are liars. Conclusion: Some politicians are liars. Is this valid?
- Valid
- Invalid (Correct answer)
- Possibly valid
- Cannot determine
Correct answer: Invalid
Invalid. The 'some promise-makers' who are liars may not include any politicians.
Politicians are a subset of promise-makers. Some promise-makers are liars. But the liars could be entirely within the non-politician portion of promise-makers. We cannot conclude any politician is a liar. The argument is invalid.
CCAT Syllogisms and Deductions 2
Premises: All athletes are disciplined.
All disciplined people are successful.
Conclusion: All athletes are successful.
Is the conclusion valid?