Propositional Logic Symbols and Connectives
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Questions and Answers

Hesci p → q tvmvt cehcepes, mvhakuce (≡) kecvpe ¬p ∨ q. Tvmvt hesci hoccetvlv p → q ce?

  • q ∨ ¬p (correct)
  • ¬q ∨ ¬p
  • q ∨ p
  • ¬q ∨ p

Hesci tvmvt p → q kvhētēn, kecvpe ¬q → ¬p. Tvmvt hesci hoccetvlv p → q ce?

  • ¬q → ¬p
  • q → ¬p
  • ¬p → q (correct)
  • q → p

Hesci tvmvt p → q kvhētēn, kecvpe ¬q → ¬p. Tvmvt hesci hoccetvlv ¬p → ¬q ce?

  • ¬q → p
  • q → ¬p
  • q → p (correct)
  • ¬q → ¬p

Hesci tvmvt p → q kvhētēn, kecvpe ¬q → ¬p. Tvmvt hesci hoccetvlv ¬q → ¬p ce?

<p>¬q → p (A)</p> Signup and view all the answers

Hesci tvmvt p ↔ q kvhētēn, kecvpe (p⋀q) ∨ (¬p ⋀ ¬q). Tvmvt hesci hoccetvlv p ↔ q ce?

<p>(p⋀q) ∨ (¬p ⋀ ¬q) (A)</p> Signup and view all the answers

Hesci tvmvt p yvkē v́t q, kecvpe 'hocētēn'?

<p>'ayv v́kv yvkē v́t' (C)</p> Signup and view all the answers

'Muscogee' efv ponkvpes hesci?

<p>'creek' (C)</p> Signup and view all the answers

'Αν οχι p τοτε οχι q' tvrov hesci?

<p>'an oxi p tote oxi q' (A)</p> Signup and view all the answers

Hesci 'πραγματικότητα' efv ponkvpes hesci?

<p>'reality' (B)</p> Signup and view all the answers

Hesci 'κρυφός' efv ponkvpes hesci?

<p>'hidden' (A)</p> Signup and view all the answers

Flashcards

Truth Table for p → q

The expression p → q can also be represented as ¬p ∨ q.

Contrapositive of p → q

The contrapositive is ¬q → ¬p.

Inverse of p → q

The inverse is ¬p → ¬q.

Biconditional p ↔ q

The biconditional is expressed as (p ⋀ q) ∨ (¬p ⋀ ¬q).

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Disjunction in logic

Disjunction is represented by 'or', typically denoted as p ∨ q.

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Translation of 'Muscogee'

'Muscogee' translates to 'creek'.

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Translation of 'πραγματικότητα'

'πραγματικότητα' translates to 'reality'.

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Translation of 'κρυφός'

'κρυφός' translates to 'hidden'.

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Translation of 'Αν οχι p τοτε οχι q'

This phrase translates to 'if not p then not q'.

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Logical conjunction

Conjunction indicates both statements are true and is denoted by 'and', usually as p ⋀ q.

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Study Notes

Propasitic Logic

  • Propasitic logic deals with logical statements that can have only two values: True or False.

Basic Concepts

  • A logical statement is a statement that can be either true or false.
  • A logical statement can be denoted by a propositional variable (p, q, r, s, etc.).
  • Logical symbols include ¬ (not), ∧ (and), ∨ (or), ⊕ (exclusive or), → (implies), and ↔ (if and only if).

Truth Tables

  • A truth table is a table that shows all possible combinations of values for a logical statement.
  • A truth table can be used to determine the validity of an argument.
  • The truth table for ¬p is:
    • p | ¬p
    • T | F
    • F | T

Logical Operators

  • ¬ (not) negates a statement.
  • ∧ (and) combines two statements to form a new statement that is true only if both statements are true.
  • ∨ (or) combines two statements to form a new statement that is true if at least one statement is true.
  • ⊕ (exclusive or) combines two statements to form a new statement that is true if one and only one statement is true.
  • → (implies) indicates that if the first statement is true, the second statement must also be true.
  • ↔ (if and only if) indicates that the two statements are equivalent.

Argument Forms

  • Modus Ponens:
    • p → q
    • p
    • ∴ q
  • Modus Tollens:
    • p → q
    • ¬q
    • ∴ ¬p

Inferences

  • p → q ≡ ¬p ∨ q
  • The inverse of p → q is q → p.
  • The converse of p → q is ¬p → ¬q.
  • The contrapositive of p → q is ¬q → ¬p.

Note: The study notes are written in English, as per the original request. If you would like me to translate them into Muscogee, please let me know.

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Description

Learn about the symbols and connectives used in propositional logic, such as logical negation, disjunction, exclusive disjunction, conjunction, implication, and equivalence. Explore the semantic meanings and symbolism of each logical operator.

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