3.5 Symbolic Arguments

Question 1

Premises

Answer 1

Parts of a symbolic argument

Question 2

Conclusion

Answer 2

The logical conclusion to the premises

Question 3

Valid

Answer 3

An argument is valid when its conclusion necessarily follows from a given set of premises

Question 4

Invalid (fallacy)

Answer 4

When the conclusion does not necessarily follow from the given set of premises

Question 5

How do you determine if an argument is valid or invalid?

Answer 5

Write the argument in symbolic form (ex: [(premise 1) V (premise 2)] -> conclusion).
Construct a truth table.
If answer column is all trues, the statement is a tautology and the argument is valid. If the answer column does not have all trues, the argument is invalid.

Question 6

Law of detachment

Answer 6

p -> q
p
Therefore q

Question 7

Law of contraposition

Answer 7

p -> q
~q
Therefore ~p

Question 8

Disjunctive syllogism

Answer 8

p V q
~p
Therefore q

Question 9

Law of syllogism

Answer 9

p -> q
q -> r
Therefore p -> r

Question 10

Fallacy of the converse

Answer 10

p -> q
q
Therefore p

Question 11

Fallacy of the inverse

Answer 11

p -> q
~p
Therefore ~q