Chapter 3.4-3.5

Question 1

Modus ponens

Answer 1

p —> q
p
∴ q

Question 2

modus Tollens

Answer 2

p —> q
~ q
∴ ~ p

Question 3

Law of syllogism

Answer 3

p —> q
q —> r
∴ p —> r

Question 4

disjunctive syllogism

Answer 4

p V q
~ p
∴ q

Question 5

fallacy of the converse

Answer 5

p —> q
q
∴ p

Question 6

fallacy of the inverse

Answer 6

p —> q
~p
∴ ~q

Question 7

Valid or invalid?

p —> q
~p
∴ ~q

Answer 7

invalid, fallacy of the inverse

Question 8

Valid or invalid?

p —> q
q
∴ p

Answer 8

invalid, fallacy of the converse

Question 9

Valid or invalid?

p V q
~ p
∴ q

Answer 9

valid, disjunctive syllogism

Question 10

Valid or invalid?

p —> q
q —> r
∴ p —> r

Answer 10

valid, Law of syllogism

Question 11

Valid or invalid?

p —> q
~ q
∴ ~ p

Answer 11

valid, modus Tollens

Question 12

Valid or invalid?

p —> q
p
∴ q

Answer 12

valid, modus ponens

Question 13

Equivalent form of:

p –> q

Answer 13

~ p V q

Question 14

Negation of Conditional

Answer 14

p Λ ~q

Question 15

Equivalent form of:

p ↔ q

Answer 15

(p —> q) Λ (q —> p)

Question 16

Converse of p —> q

Answer 16

q —> p

Question 17

Inverse of p —> q

Answer 17

~p —> ~q

Question 18

Contrapositive of p —> q

Answer 18

~q —> ~p

Question 19

What is equivalent to the converse?

Answer 19

the inverse

Question 20

What is equivalent to the inverse?

Answer 20

the converse

Question 21

What is equivalent to the contrapositive?

Answer 21

the direct conditional

Question 22

What is equivalent to the direct conditional?

Answer 22

the contrapositive