Exercise 4.1
1.
|
Give
two translations of each of the following, one using a universal quantifier,
and one using an existential quantifier. There are a number of alternative,
but equivalent, correct answers. If your answer is different from
those given, it may still be right. (Take your domain of quantification
to be everything.) |
| |
(i)
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All men are human |
| |
(ii) |
No
women like John |
| |
(iii)
|
[John
likes some women |
| |
(iv)
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Some
woman likes John |
| |
(v)
|
Only women like John. |
| |
(vi)
|
Everyone
is a man or a woman. |
| |
(vii) |
Some humans are not men. |
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(viii) |
If someone is a woman, she likes John. |
2.
|
Give two translations of each of the following, one using a universal
quantifier, and one using an existential quantifier. This time take
your domain to be humans. |
| |
(i)
|
Everyone is a woman or a man. |
|
(ii) |
Some
humans are not men |
|
