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c It is possible for a deductively sound argument to have a false conclusion.

d A valid argument cannot have true premises and a false conclusion.

e A valid argument cannot have false premises and a true conclusion.

f It is impossible for the premises of a valid argument to be true, if the conclusion is false.

g A valid argument must have true premises.

h If the conclusion of a valid argument is false, then all the premises must be false.

i If an argument has more than one premise, then if one of the premises is true, then the others must also be true.

j If a valid argument is sound, then one of its premises must be false.

k A sound argument cannot have a false premise.

I An argument cannot be both valid and sound.

m If an argument has true premises and a true conclusion, then it is valid.

n If an argument does not have true premises and a false conclusion, then it is valid.

o An argument may have true premises and a false conclusion.

8 In exercise 7, a-f, various scenarios are said to be possible or impossible. In cases where the thing is possible, give an example.

9 Rewrite the following sentences using 'if-then', so as to express the same relation between propositions. Sometimes you may have to insert or remove a 'not'.

a Either Trajan was great or Hadrian was great.

b Augustus Caesar was the greatest emperor, unless Marcus Aurelius was the greatest emperor.

c Galerius and Maximin were not both admired in Rome.

10 Can there be more than one deductively sound argument for the same conclusion? If so, give an example. If not, explain why not.

11 Consider the following two sentences:

Lee Harvey Oswald murdered John Kennedy. Lee Harvey Oswald did not murder John Kennedy.

Suppose we have two arguments, one with the first as conclusion and the other with second as conclusion. Could both arguments be valid? Could both arguments be deductively sound? Why or why not?

Chapter 3

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