M2: Prop logic and Logical Equivalence

Question 1

__ is useful for evaluating whether an argument is deductively valid as opposed to inductively valid, which is the way that people typically reason in everyday life

Answer 1

Propositional Logic

Question 2

Three kinds of symbols in formalizing propositional logic:

Answer 2

Sentence letters (ex: P, Q, R, a, b, c)
Operators/Connectives (~^v, ->, <–>)
Parenthesis

Question 3

___ is used for organization purposes, similar to parentheses in algebra and arithmetic.

Answer 3

Parentheses

Question 4

___ is one that cannot be separated into further sentences.

Answer 4

Atomical Sentence

Question 5

IMPORTANT NOTE:
1. The standard procedure is to define ___with the sentences they stand for.

Answer 5

letters

Question 6

IMPORTANT NOTE:
2. When symbolizing, one should try to break each natural language sentence into an ___

Answer 6

atomical sentence
My sister and I like coffee” could be defined:

m = My sister and I like coffee.
But also:

n = My sister likes coffee.
o = I like coffee.

Question 7

IMPORTANT NOTES
We have an operation to express “negation”. So a negative sentence will be better expressed as a ____, and later we can add the correct symbol

Answer 7

Positive sentence

Question 8

____it is a formula which is always true for every value of its propositional variables

Answer 8

Tautology

Question 9

A ___ in the English language is an expression or phrase that says the same thing twice, just in a different way.

Answer 9

tautology

Question 10

A statement, or set of statements is logically consistent when it involves no ____.

Answer 10

logical contradiction

Question 11

_____is a formula which is always false for every value of its propositional variables

Answer 11

Contradiction

Question 11

_____is a formula which is always false for every value of its propositional variables

Answer 11

Contradiction

Question 12

It is a formula which has both some true and some false values for every value of its propositional variables.

Answer 12

Contingency

Question 12

It is a formula which has both some true and some false values for every value of its propositional variables.

Answer 12

Contingency

Question 13

A formula is valid if it is____.

Answer 13

true for all values of its terms

Question 14

___ refers to the existence of a combination of values to make the expression true.

Answer 14

satisfiability

Question 15

A propositional logic is said to be satisfiable if its either a ___

Answer 15

tautology or contingency

Question 16

Hence if a logic is a ___ then it is said to be unsatisfiable.

Answer 16

contradiction

Question 17

Steps in knowing validity using truth table

Answer 17

1. Assign a letter to represent each component statement in the argument
2. Express each remises and conclusion symbolically
3. Form the symbolic statement of the entire argument by writing the conj of all premises as the antecedent of the conditional statement and the conclusion as the consequence
4. Complete the truth table for the conditional statement formed in step 3. If a tautology, then the arg is valid, otherwise, it is invalid

Question 18

VALID ARG FORMS
___ is also called “affirming the antecedent”

Answer 18

Modus Ponens

Question 18

VALID ARG FORMS
___ is also called “affirming the antecedent” because one of its premises affirms that the antecedent of the conditional is true

Answer 18

Modus Ponens

Question 19

WHAT ARG FORM?
If p is a sufficient condition of q, and p is true, then q must be true
P->Q_If there is no God, then life is meaningless.
P_____There is no god
——–
q_____Therefore, life is meaningless

Answer 19

Modus ponens

Question 20

VALID ARG FORM
___ also means “denying the consequent” because one of its premises denies that the consequent of the conditional is true

Answer 20

Modus Tollens

Question 21

WHAT ARG FORM
If q is a necessary condition of p, and q is false, then p must be false
p->q_If I’m a mom, then I’m a woman
~q___I’m not a woman
————
~p___Therefore, I’m not a mom.

Answer 21

Modus Tollens

Question 22

VALID ARG FORM
The basic form ___ gets its name from the feature from that one of the two premises is a disjunction. If one is false, then the other is true

Answer 22

disjunctive syllogism

Question 23

WHAT ARG FORM
If p is false, then q must be true.
p v q__Either I will watch a concert or I will read a novel
~p_____I will not watch a concert.
——–
q______Therefore, I will read a novel.

Answer 23

disjunctive Syllogism

Question 24

VALID ARG FORM
The arg consists of three conditionals

Answer 24

Reasoning by Transitivity (Hypothetical Syllogism)

Question 25

WHAT ARG FORM
The first conditional says that p is a sufficient condition for q.
The second one says that q in turn is a sufficient condition for r
It would then follow that p is a sufficient condition for r

p->q__If 1<2 then 2<3
q->r__If 2<3 then 2>1
____
p->r__Therefore, if 1<2 then 2>1

Answer 25

Reasoning by Transitivity (Hypothetical Syllogism)

Question 26

___are those arguments that if the arguments fall under one of these forms, there is no need to construct the truth table because it means that the arguments are invalid.

Answer 26

invalid argument forms

Question 27

INVALID ARFG FORMS
___ also called converse error and it resembles modus ponens
p->q_If I’m a mom, then I’m a woman.
q____I am a woman
——–
p____Therefore, I am a mom.

Answer 27

Fallacy of the Converse

Question 28

INVALID ARG FORMS
___ is also called inverse error. It appears very similar to a valid arg form- the contrapositive
Ex
p->q__If I’m a mom, then I’m a woman
~q____I am not a mom.
———
~q____Therefore, I am not a woman.

Answer 28

Fallacy of the inverse

Question 29

All but the final proposition are called ___.

Answer 29

premises

Question 30

The last proposition is the ___

Answer 30

conclusion

Question 31

W