Introduction to Logic: Worksheet 1 Solutions
NB: Some questions admit of more than one solution, particularly 6 and 7. If your
answer differs from that given, feel free to get in contact.
1.
a) Is not an argument; the ‘so’ does not here indicate an conclusion, but
rather that the king’s men made Humpty Dumpty into an omelette
because they couldn’t but him together again.
b) Is an argument, is not deductively valid (suppose no one dies in
tsunamis):
If God is omnipotent, he is able to prevent people from dying in
tsunamis.
If God is benevolent, he would try to prevent such death.
God is not both omnipotent and benevolent.
c) Is an argument; is deductively valid:
These cookies would have been eaten unless the Cookie Monster didn't
like them.
These cookies haven't been eaten.
The Cookie Monster does not like these cookies
2.
a) True. An argument is valid just if it is not possible for the premises to
be true and the conclusion false. Such an argument may have a false
conclusion, as long as the premises are not all true.
b) False. An argument is sound just if it is valid and has true premises. An
argument is valid just if it is not possible for the premises to be true
and the conclusion false. A valid argument with true premises must
therefore have a true conclusion. So a sound argument must have a true
conclusion.
c) False. An argument is valid just if it is not possible for the premises to
be true and the conclusion false. A valid argument with a true
conclusion may therefore have false premises, and hence fail to be
sound.
3.
4.
a) True. A pair of sentences are logically equivalent just if it is not
possible for them to differ in truth value. A sentence is logically true
just if it is not possible for it to be false. Hence any two logically true
sentences will necessarily both be true, and so it is not possible for
them to differ in truth value.
b) False. A sentence is logically indeterminate just if it is neither logically
true nor logically false. An argument is valid just if it is not possible
for the premises to be true and the conclusion false. This may be the
case when the conclusion is logically indeterminate.
