Rules of Inference

Question 1

∴

Answer 1

Therefore

Question 2

Suppose “p and q” is True. Then it must be the case that both alone are True.

Answer 2

Conjunctive Simplification

Question 3

“p ∧ q” ⇒ “p”

Answer 3

Conjunctive Simplification

Question 4

You can simplify a conjunction inside parenthesis.

Answer 4

FALSE

Question 5

The statement “The sky is blue OR I did my homework.” is True regardless of whether I did my homework or not.

Answer 5

Disjunctive Amplification

Question 6

Can mean the post-condition is True whenever the pre-condition is True.

Answer 6

⇒

Question 7

“p” ⇒ “p ∨ q”

Answer 7

Disjunctive Amplification

Question 8

You cannot amplify inside parenthesis

Answer 8

TRUE

Question 9

The sky is blue. Pigs cannot fly. Thus, the sky is blue, and pigs cannot fly.

Answer 9

Rule of Conjunction

Question 10

“(p)” ∧ “(q)” ⇒ “p ∧ q”

Answer 10

Rule of Conjunction

Question 11

When using conjunction use full statements. If negation is involved with conjunction, ___ should probably be used instead.

Answer 11

amplification

Question 12

Affirmation of an implication.

Answer 12

Modus Ponens

Question 13

Suppose we know that
▶ “If I did my homework, then I will go to the movies.” AND
▶ “I did my homework.”
Then we can affirm that “I will go to the movies.”

Answer 13

Modus Ponens

Question 14

“(p)” ∧ “(p → q)” ⇒ “q”

Answer 14

Modus Ponens

Question 15

Denying of an implication

Answer 15

Modus Tollens

Question 16

Suppose we know that
▶ “If I did my homework, then I will go to the movies.” AND
▶ “I will not go to the movies.”
Then we should be able to state that “I did not do my homework.”

Answer 16

Modus Tollens

Question 17

Ensures that implication we know to be True is not violated by a pre-condition.

Answer 17

Modus Tollens

Question 18

“(¬q)” ∧ “(p → q)” ⇒ “¬p”

Answer 18

Modus Tollens

Question 19

Satisfying a Disjunction using partial information.

Answer 19

Disjunctive Syllogism

Question 20

Suppose we know that
▶ “I did not do my homework or I will go to the movies.” AND
▶ “I did my homework.”
Then we should be able to state that “I will go to the movies.”

Answer 20

Disjunctive Syllogism

Question 21

Ensures that a Disjunction remains True, if one part is False.

Answer 21

Disjunctive Syllogism

Question 22

“(¬p)” ∧ “(p ∨ q)” ⇒ “q”

Answer 22

Disjunctive Syllogism

Question 23

Implication has a transitive sort of behavior.

Answer 23

Syllogism

Question 24

Suppose we know that
▶ “If I do my homework, then I will pass.” AND
▶ “If I pass, then I will go to the movies.”
Then we should be able to state that “If I do my homework, then I will go to the movies.”

Answer 24

Syllogism

Question 25

“(p → q)” ∧ “(q → r)” ⇒ “p → r”.

Answer 25

Syllogism

Question 26

To show equivalence using Rules of Inference…

Answer 26

2 proofs are needed

▶ The forward direction (⇒)
▶ The reverse direction (⇐)