Exam #2

Question 1

Modus Ponens

Answer 1

P → Q
P
∴Q

Question 2

Modus Tollens

Answer 2

P→Q
¬Q
∴ ¬P

Question 3

Generalization

Answer 3

P
∴ P ∨ Q
Q
∴ P ∨ Q

Question 4

Specialization

Answer 4

P ∧ Q
∴ P
P ∧ Q
∴ Q

Question 5

Elimination

Answer 5

P ∨ Q
¬Q
∴ P
P ∨ Q
¬P
∴ Q

Question 6

Transitivity

Answer 6

P → Q
Q → R
∴ P → R

Question 7

Conjunction

Answer 7

P
Q
∴ P ∧ Q

Question 8

Argument

Answer 8

a sequence of statements called
premises, followed by a final statement called the
conclusion.

Question 9

Valid Argument

Answer 9

An argument (or argument form) is valid if every
truth assignment that makes the premises true also makes
the conclusion true. (Otherwise, we say that the argument is
invalid.)

Question 10

Fallacies

Answer 10

errors in reasoning that result in invalid arguments

Question 12

Divisibility

Answer 12

A nonzero integer m divides an integer n if there is
an integer q such that n = m · q

Question 13

Proof

Answer 13

a convincing argument that some mathematical statement is true

Question 14

Axiom

Answer 14

some mathematical statement that is generally accepted without proof

Question 15

Definition

Answer 15

an agreement about the meaning of a term

Question 16

Conjecture

Answer 16

a statement that we believe might be true but that have not yet proved

Question 17

Theorem

Answer 17

a mathematical statement for which we have a proof

Question 18

Lemma

Answer 18

a mathematical statement that was proven mainly to help with proving some theorem

Question 19

Congruence

Answer 19

Let n be an integer. If a and b are integers, then we say that a is congruent to b modulus n provided that n divides a-b

Question 20

Methods of indirect proof

Answer 20

contrapositive and contradiction

Question 21

Parity Property

Answer 21

each integer is either even or odd (and not both)

Question 22

Negation of a conditional

Answer 22

¬(P→ Q) ≡ P ∧ ¬Q

Question 23

Contrapositive

Answer 23

P → Q ≡ ¬Q → ¬P