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intro to logic > proofs > Flashcards

proofs Flashcards

1
Q

a demonstration that an argument is invalid/ valid

A

proof

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2
Q

true or false: a proof is an argument

A

false

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3
Q

what makes a good proof?

A

obvious and valid

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4
Q

how to prove an invalidity?

A

informal proof with counterexample

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5
Q

eliminates wide scope conjunction.

A

&Elim; 1
- cites one line

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6
Q

introduce a conjunction

A

&Intro;1,2
- cites TWO lines

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7
Q

eliminate 2 stacked negations

A

~Elim;1
- only applies to main connective

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8
Q

build a disjunction from a disjunct

A

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

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9
Q

reiteration

A

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

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10
Q

how to reason from a disjunction?

A

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

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11
Q

how to reason to a negation?

A

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

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12
Q

true or false: only a contradiction can entail a contradiction

A

true

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13
Q

what is the 5 step plan?

A
  1. pick a disjunct
  2. put it in a subproof
  3. build the disjunction
  4. intro the #
  5. intro the ~
    always ends with ~Intro!!!
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14
Q

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

A

reductio!
- never assume what you already know

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15
Q

2 more weird cases of validity

A
  • logically false premise
  • conclusion same as premise
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16
Q

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

A

false

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17
Q

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

A

true

18
Q

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

A

true

19
Q

place the sentence: some dog is a police dog

A

contingent truth

20
Q

place the sentence: all police dogs are dogs

A

logical truth

21
Q

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

A

tautology

22
Q

place the sentence: all dogs are police dogs

A

contingent falsity

23
Q

place the sentence: some police dog isnt a dog

A

logical falsity

24
Q

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

A

taut-falsity

25
Q

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

A

contradiction trick
reiteration trick
reductio
build P->Q

26
Q

what is the reiteration trick?

A

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

27
Q

how to reason from a universal quantifier?

A

universal instantiation
AIntro

28
Q

how do you reason to an existential?

A

Existential generalization
EIntro

29
Q

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

A

AELim

30
Q

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

A

arbitrary names

31
Q

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

A

universal generalization

32
Q

how to reason from an existential claim?

A

existential instantiation

33
Q

how do you use =Elim?

A

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

34
Q

true or false: a logically true conclusion follows from anything

A

true

35
Q

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

A

AElim

36
Q

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

A

AIntro

37
Q

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

A

start EElim

38
Q

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

A

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

39
Q

how would you prove ~ExP(x)?

A

reductio

40
Q

how would you prove ~AxP(x)?

A

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

intro to logic (6 decks)

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