proofs

Question 1

a demonstration that an argument is invalid/ valid

Answer 1

proof

Question 2

true or false: a proof is an argument

Answer 2

false

Question 3

what makes a good proof?

Answer 3

obvious and valid

Question 4

how to prove an invalidity?

Answer 4

informal proof with counterexample

Question 5

eliminates wide scope conjunction.

Answer 5

&Elim; 1
- cites one line

Question 6

introduce a conjunction

Answer 6

&Intro;1,2
- cites TWO lines

Question 7

eliminate 2 stacked negations

Answer 7

~Elim;1
- only applies to main connective

Question 8

build a disjunction from a disjunct

Answer 8

vIntro;2
- disjuncts can be complex sentences
- can add as much as you want at a time from one disjunct

Question 9

reiteration

Answer 9

Reit;1
- requires line number
- valid from circular reasoning

Question 10

how to reason from a disjunction?

Answer 10

vElim;1, 2-3, 4-5
- proof by cases
- requires citation of disjunction and subproofs of both disjuncts
- requires the exact same sentence to appear 3 times: in each subproof AND in the main proof

Question 11

how to reason to a negation?

Answer 11

reductio!!!
- ~Intro;2-7
- cites entire subproof
- make temporary assumption and show that a contradiction results
- each subproof ends with #

Question 12

true or false: only a contradiction can entail a contradiction

Answer 12

true

Question 13

what is the 5 step plan?

Answer 13

1. pick a disjunct
2. put it in a subproof
3. build the disjunction
4. intro the #
5. intro the ~
   always ends with ~Intro!!!

Question 14

how do you prove a tautology (no premises) in bool?

Answer 14

reductio!
- never assume what you already know

Question 15

2 more weird cases of validity

Answer 15

• logically false premise
• conclusion same as premise

Question 16

true or false: if an argument is unsound, then it is invalid

Answer 16

false

Question 17

true or false: a contingently false premise can entail a logically true conclusion

Answer 17

true

Question 18

true or false: a logically true premise cannot entail a contingently true conclusion

Answer 18

true

Question 19

place the sentence: some dog is a police dog

Answer 19

contingent truth

Question 20

place the sentence: all police dogs are dogs

Answer 20

logical truth

Question 21

place the sentence: rufus is a police dog or isnt a police dog

Answer 21

tautology

Question 22

place the sentence: all dogs are police dogs

Answer 22

contingent falsity

Question 23

place the sentence: some police dog isnt a dog

Answer 23

logical falsity

Question 24

place the sentence: rufus is a dog and is not a dog

Answer 24

taut-falsity

Question 25

what do you do when you have a negation around a conditional? ~(P->Q)

Answer 25

contradiction trick reiteration trick reductio build P->Q

Question 26

what is the reiteration trick?

Answer 26

~(P->Q) ==> P&~Q - use REIT to build P->Q

Question 27

how to reason from a universal quantifier?

Answer 27

universal instantiation AIntro

Question 28

how do you reason to an existential?

Answer 28

Existential generalization EIntro

Question 29

allows you to replace every instance of the variable with a name

Answer 29

AELim

Question 30

name we declare to stand for an arbitrary member of the domain

Answer 30

arbitrary names

Question 31

inferring something is true for all objects once we prove it is true for an arbitrary object - starts w arbitrary assumption @n

Answer 31

universal generalization

Question 32

how to reason from an existential claim?

Answer 32

existential instantiation

Question 33

how do you use =Elim?

Answer 33

must cite 2 things: thing you are eliminating and the sentence you are doing the substitution into - allows you to substitute one or more occurences of a name G(p) premise p = a premise G(a) =Elim;1,2

Question 34

true or false: a logically true conclusion follows from anything

Answer 34

true

Question 35

what would your strategy be for a proof with a universal premise?

Answer 35

AElim

Question 36

what would your strategy for a proof with a universal conclusion?

Answer 36

AIntro

Question 37

what would your strategy be for a proof with an existential premise?

Answer 37

start EElim

Question 38

what would your strategy be for a proof with an existential conclusion?

Answer 38

wait! look around for other ideas. you will use EIntro at some point

Question 39

how would you prove ~ExP(x)?

Answer 39

reductio

Question 40

how would you prove ~AxP(x)?

Answer 40

-start w reductio -use 5 step plan to reductio assumption ~(~Pv~Q) -assume ~Ex~P(x)