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logic test

Answers

Answer 1.
a) All ducks quack.
b) Donald is a duck.
- Therefore: Donald quacks.

Valid.

Answer 2.
a) All female logicians are clear thinkers.
b) All lawyers are clear thinkers.
- Therefore all female logicians are lawyers.

Invalid.

Answer 3.
a) Men think only about sex.
b) A man called Gary is thinking.
- Therefore Gary is thinking about sex.

Valid. Remember validity is not the same as truth. The premise, 'men only think about sex' is a bit fishy, to say the least. A false premise can produce a false conclusion, but the argument can still be valid.

Answer 4.
a) Where there is poverty there is crime.
b) There is poverty in Camberwell.
- Therefore there is crime in Camberwell.

Valid.

Answer 5.
a) Where there is poverty there is crime.
b) There is crime in Camberwell.
- Therefore there must be poverty in Camberwell.

Invalid. There may be crime where there is poverty, but it does not necessarily follow that wherever crime is there is poverty.

Answer 6.
a) Some mammals are marsupials.
b) All kangaroos are mammals.
- Therefore all kangaroos are marsupials.

Invalid.

Answer 7.
a) All ducks bark.
b) Donald is a duck.
- Therefore Donald barks.

Valid (but not true!).

Answer 8.
a) When I get hungry I could eat a horse.
b) I am hungry now.
- Therefore I should eat a horse.

Invalid. If the first premise contained the word 'should' instead of 'could', then the argument would have been valid.

Answer 9.
a) Blue and yellow make green.
b) Blue and red make brown.
- Therefore blue and white make sky blue.

Invalid. Not a proper argument.

Answer 10.
a) Jenny lives in Paris.
b) Paris is in New Zealand.
- Therefore Jenny lives in New Zealand.

Valid (but not true because Paris is not in New Zealand!)

Answer 11.
a) Men are from Mars.
b) Women are from Venus.
- Therefore men and women will never understand each other.

Invalid. (If men and women could never understand each other then the author could never have written his book.)

Answer 12.
a) The man was stabbed to death.
b) Mary was seen leaving the scene of the crime shortly after the time of the murder.
c) Blood found on Mary's trousers was the same as the victim's.
d) Only Mary's fingerprints were found on the murder weapon.
e) No other people were witnessed near the scene of the crime.
f) Mary's DNA was found on the victim's body.
g) The CCTV evidence showed only Mary entering and leaving the victim's flat.

Invalid. This is invalid because although all the evidence points to Mary as committing the murder, there could still be another possible explanation. Sherlock Holmes made his name in such cases. Because there could be another solution, the argument cannot be called deductive. However, when an argument is very strong but not conclusive it is called an argument from induction. The conclusion is accepted because the evidence favours it and there is little or no evidence to support an alternative conclusion.

Answer 13.
a) Only language users employ generalisations.
b) Not a single animal uses language.
c) At least some animals reason.

Invalid. But we can say that 'not all' reasoning beings employ generalisations.

Answer 14.

diagram for Q14The results from a logic test taken by 500 women and 500 men showed that:

a) Some women are more logical than some men.
b) Some men are more logical than some women.
c) The top ten performers were all women.
d) The bottom ten performers were all men.

Invalid. This conclusion can't be drawn because the results could have been as shown in diagram.

Until we see the full details of the survey, we can't be sure that the results above did not occur. What conclusion would be drawn if that was the case?

 

Answer 15.
a) Water is a molecule composed of two hydrogen atoms and one oxygen atom.
b) Every observation or examination by microscope has confirmed this.

Conclusion
Therefore we can predict that every future examination of water will reveal the same chemical composition.

Invalid. The syllogism itself is invalid and can only be considered as a strong inductive argument and not deductive. It is the 'we can predict' part of the conclusion which comes from nowhere, so the argument is not strictly formal. There is an ongoing debate within philosophical circles as to whether water must conform to the molecule H2O. Some argue that it is logically possible for a substance to appear exactly as water and yet still be of a different chemical composition.

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