Propositions and Truth Tables Quiz
9 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is a proposition?

A proposition is a sentence that is either true or false, but not both simultaneously.

The sentence 'The integer x divides 2' is a proposition.

False

What is the truth value assigned to a true proposition?

1 or T

What is the truth value assigned to a false proposition?

<p>0 or F</p> Signup and view all the answers

What is a predicate?

<p>A predicate is a logical formula that depends on a free variable.</p> Signup and view all the answers

What does the negation of P (¬P) represent?

<p>True if P is false</p> Signup and view all the answers

Match the logical connectives with their definitions:

<p>Negation = Not P Conjunction = P and Q Disjunction = P or Q</p> Signup and view all the answers

When is a conjunction (P ∧ Q) true?

<p>If both P and Q are true</p> Signup and view all the answers

When is a disjunction (P ∨ Q) false?

<p>If both P and Q are false</p> Signup and view all the answers

Study Notes

Proposition (statement), Truth Table

  • Definition: A proposition is a sentence that can be definitively true or false, but not both.
  • Notation: Propositions are represented using letters: P, Q, R, etc.
  • Examples:
    • "For all real numbers x, x² ≥ 0" (True proposition)
    • "2 x 3 = 5" (False proposition)
    • "The integer x divides 2" (Not a proposition, as it depends on the value of x)
  • Truth Values:
    • True propositions are assigned the value 1 (or T).
    • False propositions are assigned the value 0 (or F).

Truth Table

  • Definition: A truth table displays the truth values of a proposition for all possible combinations of truth values of its components.
  • Example: Truth table for a proposition P:
P
1
0

Predicate

  • Definition: A predicate is a logical formula that depends on one or more free variables. The truth value of a predicate is determined by assigning specific values to its variables.

Basic Logical Connectives

a) Negation

  • Notation: "¬P" or "Not P"
  • Definition: The negation of a proposition P is true if P is false, and false if P is true. It essentially reverses the truth value of P.
  • Truth Table:
P ¬P
1 0
0 1
  • Examples:
    • Given P: "2 × 3 = 6", its negation ¬P is "2 × 3 ≠ 6".
    • Given Q: "√2 ∈ N" (√2 is a member of the set of natural numbers), its negation ¬Q is "√2 ∉ N" (√2 is not a member of the set of natural numbers).

b) Conjunction

  • Notation: "P ∧ Q" or "P and Q"
  • Definition: The conjunction of propositions P and Q is true only if both P and Q are true. Otherwise, it's false.
  • Truth Table:
P Q P ∧ Q
1 1 1
1 0 0
0 1 0
0 0 0
  • Examples:
    • "π is not an integer and π > 2"
    • "f(x) is decreasing and f(x) = e^x"

c) Disjunction

  • Notation: "P ∨ Q" or "P or Q"
  • Definition: The disjunction of propositions P and Q is false only if both P and Q are false. Otherwise, it's true.
  • Truth Table:
P Q P ∨ Q
1 1 1
1 0 1
0 1 1
0 0 0
  • Examples:
    • "π ≥ 2 or e > 1"
    • "π = 3 or e < 2"

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

Description

Test your understanding of propositions, truth values, and truth tables. Learn how to differentiate between true propositions and predicates, as well as how to construct truth tables for logical statements. This quiz will help solidify your knowledge in foundational logic concepts.

More Like This

Truth Tables Lecture
16 questions
Logique Propositionnelle - Définitions
16 questions
Lógica Proposicional en Matemáticas
37 questions
Proposiciones y Conectivos Lógicos
40 questions

Proposiciones y Conectivos Lógicos

MagnanimousLapSteelGuitar avatar
MagnanimousLapSteelGuitar
Use Quizgecko on...
Browser
Browser