introduction to logic jennifer wang fall 2009 midterm review quiz game
TRANSCRIPT
![Page 1: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/1.jpg)
INTRODUCTION TO LOGICJennifer Wang
Fall 2009Midterm Review
Quiz Game
![Page 2: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/2.jpg)
Concepts True/False TranslationsInformal Proofs
Formal Proofs
100 100 100 100 100
200 200 200 200 200
300 300 300 300 300
400 400 400 400 400
500 500 500 500 500
![Page 3: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/3.jpg)
Final Question
![Page 4: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/4.jpg)
(100)
If A is a tautology, is it also a logical truth?
Yes.
![Page 5: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/5.jpg)
(200)
How do you check if an argument is valid using truth tables?
Check all the rows in which the premises are all true. If the conclusion is always also true, it’s valid. If there’s a row where the premises are all true but the conclusion is false, it’s invalid.
![Page 6: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/6.jpg)
(300)
Why is disjunction introduction a valid form of inference?
By the truth table for , P Q is true iff at least one of P or Q is true. If we already know that P is true, we know that P Q is true.
![Page 7: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/7.jpg)
(400)
Name three of the four formal proof methods we’ve learned so far that use subproofs.
Disjunction elimination (proof by cases)
Negation introduction (proof by contradiction)Conditional introduction (conditional proof)Biconditional introduction (biconditional proof)
![Page 8: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/8.jpg)
(500)
What does it mean for a connective to be truth-functional?
This means that we can determine the truth value of the connective from the truth values of its parts.
![Page 9: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/9.jpg)
(100)
What is the main connective in this sentence?: (Small(a) Small(b) Small(c)) Small(d)
Disjunction.
![Page 10: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/10.jpg)
(200)
How does this translate into FOL?: c is left of and to the back of b only if b is a cube..
(LeftOf(c,b) BackOf(c,b)) Cube(b)
![Page 11: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/11.jpg)
(300)
How does this translate into FOL?: Homer is a Simpson but Marge is truly a Simpson also.
Simpson(homer) Simpson(marge)
![Page 12: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/12.jpg)
(400)
How does this translate into FOL? If d is a cube, then it is not in the same column as either a or b.
Cube(d) (SameCol(d,a) SameCol(d,b))
![Page 13: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/13.jpg)
(500)
How does this sentence read in plain English?: Red(mars) (Red(earth) Red(jupiter))
Mars is red if and only if not both Earth and Jupiter are red.
![Page 14: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/14.jpg)
(100)
A valid argument can have false premises.
True.
![Page 15: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/15.jpg)
(200)
Provided that Jane runs, Ron does not fall translates as: Runs(jane) Falls(ron)
False.
![Page 16: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/16.jpg)
(300)
This equivalence holds: (Q P) iff Q P
True.
![Page 17: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/17.jpg)
(400)
This equivalence holds:P Q iff (P Q) (P Q)
False.
![Page 18: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/18.jpg)
(500)
This sentence is true in this world: SameCol(a,b) (Cube(a) Tet(b))
True.
![Page 19: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/19.jpg)
(100)
What is the informal correlate of this rule: = Elim?
Indiscernibility of Identicals
![Page 20: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/20.jpg)
(200)
How many cases do you need in a proof by cases?
How many ever disjuncts there are in the disjunction you’re using.
![Page 21: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/21.jpg)
(300)
Which ones of these informal rules do not correspond to a formal rule?: Disjunctive syllogism, modus ponens, modus tollens, reflexivity of identity
Disjunctive syllogism, modus tollens
![Page 22: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/22.jpg)
(400)
Is this a valid argument? Explain why or why not.
Yes. Premise 2 is equivalent to Small(a) Small(b), so Small(b) follows by modus ponens. By 3 and modus tollens, we get Small(c), or Small(c). By this and premise 4, Small(d) follows from disjunctive syllogism, which is our conclusion.
![Page 23: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/23.jpg)
(500)
Give an informal proof of this argument, citing all rules and their justifications.
Let’s do a proof by cases on premise 3. Case 1: Assume that A. From this and premise 1, B follows by modus ponens. Case 2: Assume that C. This is equivalent to C by double negation. From this and premise 2, B follows by modus tollens. But by double negation, this is just B. So either way B follows, which is the conclusion we want.
![Page 24: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/24.jpg)
(100)
What is the name of the method of inference used here?
Disjunction elimination (proof by cases)
![Page 25: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/25.jpg)
(200)
What do you need to cite for a proof of P Q?
Two subproofs, one going from P to Q and one going from Q to P.
![Page 26: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/26.jpg)
(300)
There are two places to go after you derive the contradiction symbol. What are they?
You can use contradiction elimination to derive anything you want, or if you’re in a subproof, you can finish the subproof you’re in and derive the negation of the assumption that led to the contradiction (negation introduction).
![Page 27: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/27.jpg)
(400)
Give a formal proof of this argument:
![Page 28: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/28.jpg)
(500)
Give a formal proof of this argument:
![Page 29: INTRODUCTION TO LOGIC Jennifer Wang Fall 2009 Midterm Review Quiz Game](https://reader036.vdocument.in/reader036/viewer/2022062422/56649f265503460f94c3e11b/html5/thumbnails/29.jpg)
Final question
Give an example of an argument where the conclusion is a logical but not tautological consequence of some premises. Give an informal or formal proof of the argument (your choice), and then construct a truth table to show this result. Make sure to write down your explanation of why it’s a logical but not tautological truth.