2.3

Question 1

For an argument to be valid means that every argument of the same form whose premises _____ has a _____ conclusion

Answer 1

all are true; true

Question 2

For an argument to be invalid means that there is an argument of the same form whose premises _____ and whose conclusion ______

Answer 2

are all true; is false

Question 3

For an argument to be sound means that it is _____ and its premises _____. In this case we can be sure that its conclusion _____.

Answer 3

valid; all are true; is true

Question 4

Premises

Answer 4

everything given before conclusion sentence (always true)

Question 5

Modus Ponens

Answer 5

p -> q
p
:: q

Question 6

Modus Tollens

Answer 6

p -> q
~q
:: ~p

Question 7

Generalization

Answer 7

p
:: p \/ q
or
q
:: p \/ q

Question 8

Specialization

Answer 8

p /\ q
:: p
or
p /\ q
:: q

Question 9

Elimination

Answer 9

p \/ q
~p
:: q
or
p \/ q
~q
:: p

Question 10

Conjunction

Answer 10

p
q
:: p /\ q

Question 11

Transitivity

Answer 11

p -> q
q -> r
:: p -> r

Question 12

Proof by division into cases

Answer 12

p \/ q
p -> r
q -> r
:: r

Question 13

Contradiction Rule

Answer 13

~p -> c
:: p

Question 14

converse error

Answer 14

p -> q
q
:: p
INVALID

Question 15

inverse error

Answer 15

p -> q
~p
:: ~q
INVALID