Exam #2

Question 1

Tautology

Answer 1

statement that is always true

Question 2

Co-domain

Answer 2

set of all possible values which can occur from a mapping from a set A to a set B

Question 3

Range

Answer 3

set of values that actually occur from a mapping from a set A to a set B

Question 4

Premises

Answer 4

Everything given before conclusion sentence

Question 5

Modus Ponens

Answer 5

if p then q
p
:: q

Question 6

Modus Tollens

Answer 6

if p then q
~q
:: ~p

Question 7

Generalization

Answer 7

p
:: p \/ q

Question 8

Specialization

Answer 8

p /\ q
:: p

Question 9

Elimination

Answer 9

p \/ q
~q
:: p

Question 10

Transitivity

Answer 10

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

Question 11

Converse error

Answer 11

if p then q
q
:: p
INVALID

Question 12

Inverse error

Answer 12

if p then q
~p
:: ~q

Question 13

predicate

Answer 13

sentence that contains a finite # of variables and becomes a statement when specific values are substituted for the variables

Question 14

Dents

Answer 14

between any two real #s there is another

Question 15

reciprocals

Answer 15

multiplicitive inverses

Question 16

opposites

Answer 16

additive inverses

Question 17

Universal instantiation

Answer 17

if a property is true of everything in a set, then it is true of any particular thing in the set

Question 18

closure

Answer 18

likelihood of an operation on elements of a set

Question 19

proof by division into cases

Answer 19

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