Test 1

Question 1

Contrapositive

Answer 1

P ➞ q

CP : ~q ➞ ~p

Question 2

Converse

Answer 2

P ➞ q

Con : q ➞ p

Question 3

Inverse

Answer 3

P ➞ q

Inv : ~p ➞ ~q

Question 4

Modus tollens

Answer 4

if p then q
~q
therefore ~p

Valid argument form

Question 5

Modus ponens

Answer 5

If p then q
p
therefore q

Question 6

Generalization

Answer 6

Rule of inference

p
therefore p or q

q
therefore q or p

Question 7

Specialization

Answer 7

Rule of inference

p ^ q
therefore p

p ^ q
therefore q

Question 8

Conjunction

Answer 8

Rule of inference

p
q
therefore p ^ q

Question 9

Elimination

Answer 9

Rule of inference

p v q
~q
therefore p

p v q
~p
therefore q

Question 10

Transitivity

Answer 10

Rule of inference

p ➞ q
q ➞ r
therefore p ➞ r

Question 11

Proof by division into cases

Answer 11

Rule of inference

p v q
p ➞ r
q ➞ r
therefore r

Question 12

r is a sufficient condition for s

Answer 12

Means:

If r, then s

(r ➞ s)

Question 13

r is a necessary condition for s

Answer 13

Means:

If not r, then not s

(~r ➞ ~s)

(~r ➞ ~s == s ➞ r)

Question 14

r is a necessary and sufficient condition for s

Answer 14

Means:

r if and only if s

(r s)