Propositions

• Discrete variables represent counts (e.g. the number of objects in a collection).
• A discrete variable is a variable that takes on distinct, countable values.
• Continuous variables represent measurable amounts (e.g. water volume or weight).
• A continuous variable is a variable that takes on any value within a range, and the number of possible values within that range is infinite. 
• Definition of Discrete Structures: According to Polya (1983) and Larson (1985), “The problem solving is an art at this point and there are no universal approaches one can take to solving problems.”
• Logic is the technique by which we add conviction to truth. -Jean De La Bruyère.
• The propositions will be known as the atomic propositions if it will not further divided. This type of proposition is also known as the simple proposition
• The propositions will be known as compound propositions if they are formed by the combination of one or more atomic propositions with the help of connectives.
• Statements that are NOT Propositions

  • Command
  • Question
  • Exclamation
  • Based on individual preference
  • Predicate (Finite number of variable)
• Negation (not)

  • Denoted ¬
• Conjunction (and)

  • Denoted ∧
• Disjunction (or)

  • Denoted ∨
• Conditional (if then or implication)

  • Denoted →
• Biconditional (if and only if or double implication)

  • Denoted ↔
• Syntax refers to the formal rules and structure of a mathematical system or language. It focuses on the arrangement and organization of symbols, expressions, and formulas within the system.
• Semantics, on the other hand, deals with the meaning and interpretation of expression and formulas within a mathematical system. It focuses on understanding the truth values and relationships between objects or statements.
• A truth table is a tabular representation of all the combinations of values for inputs and their corresponding outputs. It is a mathematical table that shows all possible outcomes that would occur from all possible scenarios that are considered factual, hence the name.