TASK 8 - PROPOSITIONAL LOGIC Flashcards Preview

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Flashcards in TASK 8 - PROPOSITIONAL LOGIC Deck (32)
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1
Q

propositional logic

A

= fundamental elements are whole statements (propositions)

  • statements are represented by letters
  • statements are combined by means of the operators to represent more complex statements
2
Q

simple statement

A

= one that does not contain another statement as a component (e.g. fastfood is unhealthy’)
- statement is represented by an uppercase letter

3
Q

compound statement

A

= one that contains at least one simple statement as a component (e.g either people get serious about conversation (1) or energy prices will rise (2))
- each statement is represented by an uppercase letter

4
Q

logical operators

- main operator

A

= operator that has as its scope everything else in the statement

1) either the only one
2) if there are NO parentheses: the only one that is not a tilde ∼/¬
3) if there are parentheses: the one that lies outside of them

5
Q

logical operators

- tilde (∼)/¬

A

= negation
= not, it is not the case that
- always in front of the proposition it negates
- true if: false

6
Q

logical operators

- dot (⋅)/∧

A

= conjunction
= and, also, moreover
- true if: both true

7
Q

logical operators

- wedge (∨)/I

A

= disjunction
= or, unless
- inclusive: both possibilities are allowed to happen at the same point
- true if: one of the two OR both true

8
Q

logical operators

- horseshoe (⊃)/–>

A

= implication; conditionals
= if…then, only if
- true if: the second is true OR the first one is false

9
Q

conditionals

A

= expresses the relation of material implication

  • antecedent = first letter
  • -> statement following ‘if’
  • consequent = second letter
  • -> statement following ‘only if’
10
Q

conditionals

- sufficient condition

A

= A is sufficient for event B whenever the occurrence of A is ALL THAT IS REQUIRED for the occurrence of B
- placed in the antecedent of the conditional

11
Q

conditionals

- necessary condition

A

= A is necessary for B because B CANNOT OCCUR WITHOUT occurrence of A
- placed in the consequent

12
Q

logical operators

- triple bar (≡)/

A

= equivalence; biconditionals
= if and only if; then and only then
- true if: both true OR both false

13
Q

propositions

A

= statements that can be either true or false

14
Q

truth value

A

= function of the truth value of its components

15
Q

truth function

A

= any compound propositions whose truth value is completely determined by the truth values of its components

16
Q

truth tables

A

= arrangement of truth values that show every possible case how the truth value of a compound proposition is determined by the truth values of its simple components

17
Q

statement variables

A

= lowercase letters that can stand for any compound statement (truth value of combination)
- if P and Q true: P ∧ Q also true

18
Q

compute truth value of longer propositions

A
  1. enter truth values of simple components directly beneath the letters
  2. then use these truth values to compute the truth values of the compound components
  3. the truth value of a compound statement is written beneath the operator representing it
19
Q

tautology

A

= logically true = tautologous statement

= statement which is always true

20
Q

contradiction

A

= logically false

= proposition which is always false

21
Q

contingency

A

= proposition which is sometimes true and sometimes false

22
Q

equivalence

A

= two statements are logically equivalent if they have the same truth value on each line under their main operators

23
Q

consistency

A

= if there is at least one line on which both (or all) of them turn out to be true

24
Q

inconsistency

A

= no line on which both (or all) are true

25
Q

valid argument forms

- disjunctive syllogism

A
= one of the premises presents two alternatives and the other eliminates one of them (method of elimination) 
P ∨ Q
∼/¬ P
-----
Q
26
Q

valid argument forms

- pure hypothetical syllogism

A
= two premises and one conclusion, all of which are hypothetical (conditional) statements
P ⊃/--> Q
Q ⊃/--> R
-----
P ⊃/--> R
27
Q

valid argument forms

- modus ponens (MP)

A
= a conditional premise, a second premise that asserts the antecedent of the conditional premise and a conclusion that asserts the consequent
P ⊃/--> Q
P
-----
Q
28
Q

valid argument forms

- mous tollens (MT)

A
= a conditional premise, a second premise that denies the consequent of the conditional premise and a conclusion that denies the antecedent
P ⊃/--> Q
∼/¬ Q
-----
∼/¬ P
29
Q

valid argument forms

- constructive dilemma

A
= a conjunctive premise made up of two conditional statements, a disjunctive premise that asserts the antecedents in the conjunctive premise (like MP) and a disjunctive conclusion that asserts the consequence of the conjunctive premise 
(P ⊃/--> Q) ⋅/∧ (R ⊃/--> S)
P ∨ R
-----
Q ∨ S
30
Q

valid argument forms

- destructive dilemma

A

(P ⊃/–> Q) ⋅/∧ (R ⊃/–> S)
∼/¬Q ∨ ∼/¬S
—–
∼/¬P ∨ ∼/¬R

31
Q

fallacies/invalid argument forms

- affirming the consequent

A
= a conditional premise, a second premise that asserts the consequent of the conditional and a conclusion that asserts the antecedent 
P ⊃/--> Q
Q
-----
P
32
Q

fallacies/invalid argument forms

- denying the antecedent

A

P ⊃/–> Q
∼/¬ P
—–
∼/¬ Q