W2 Proposition

• Discrete Structure


  The study of mathematical structures that are discrete rather than continuous
• Discrete


  • Counting the number of people in a room
  • Measuring the weight of an object in kilograms
• Continuous


  • Measuring the temperature of a liquid
  • Tracking the speed of a moving car
• Proposition


  A statement that is either true or false
• Atomic Propositional Logic


  Propositions that cannot be further divided
• Compound Propositions


  Propositions formed by combining one or more atomic propositions with logical connectives
• Statements that are not propositions include questions, commands, and exclamations
• Logical Connectives


  Symbols used to combine propositions, including negation (¬), conjunction (∧), disjunction (∨), implication (→), and biconditional (↔)
• Syntax


  The formal rules and structure of a mathematical system or language
• Semantics


  The meaning and interpretation of expressions and formulas within a mathematical system
• Truth Table


  A table that shows all possible combinations of input values and the corresponding output values for a logical statement. Used to illustrate the logical relationships between propositions using the logical connectives (negation, conjunction, disjunction, implication, biconditional)
• What are the four Mathematical Logics Classification?

  Set Theory

  Model Theory

  Recursion Theory

  Proof Theory
• Propositional Logic is the study of the logical form of propositions.
• What are the types of Propositional Logic?

  Atomic Propositional Logic

  Compound Proposition

  Conditional Proposition

  Disjunction

  Biconditional
• It is a declarative statement and studies the relationship between two or more propositions. 


  Propositional Logic
• What do we use to denote propositional variables that represents propositions?

  Letters
• What do you call as the building blocks of logic, a statement that is either true or false but not both?

  Proposition
• It is a particular mode of reasoning viewed as valid or faulty.

  Logic
• What are the applications of logic?

  Problem Solving

  Decision Making

  Critical Thinking

  Mathematical Reasoning

  Computing and Technology
• A proposition is said to be atomic or simple if it cannot be further subdivided.