1. a. A sentence is logically true if and only if it cannot be denied without contradiction.
b. An argument is deductively valid if and only if it would be contradictory to suppose that the
premises are true and the conclusion false. An argument is deductively invalid if and only if it is
not deductively valid.
c. The members of a pair of sentences are logically equivalent if and only if there is a
contradiction in supposing that one of the sentences is true while the other sentence is false.
2. a. This sentence does have a truth-value (as it happens, the value ‘false’).
b. This sentence is a curse. It has no truth-value.
c. This marginally grammatical sentence might be an instruction to police officers, in which case
it does not have a truth-value. It might also be a warning to motorists, in which case it does have
d. This is a bit of advice. It has no truth-value.
3. a. There is an argument here:
That boxer is moving well and throwing hard punches.
That boxer cannot be hurt too badly.
The argument is deductively invalid. (The boxer may have injuries that are not apparent, so we
can assume that the premise is true and the conclusion is false without running into a
contradiction.) It does have considerable inductive strength.
b. This is not an argument. It is a claim, probably a true one, that certain behavior in bridge is
c. This is an argument:
Either the members of the electoral college do their job or they don’t.
If the members of the electoral college do their job, then they are useless.
If the members of the electoral college don’t do their job, then they are danger