Propositional and Predicate Logic

Propositional Logic

• A proposition is a declarative sentence that is either true or false, but not both.
  • Examples:
    • Kuala Lumpur is the capital of Malaysia. (True)
    • Perak is the biggest state in Malaysia. (False)
    • $1 + 1 = 2$ (True)
    • $2 + 2 = 3$ (False)
  • Non-propositions:
    • What time is it?
    • Read this carefully.
    • $x + 1 = 2$
    • $x + y = z$
• Propositional variables are denoted by letters like p, q, r, s, …
• True propositions have a truth value of True (T).
• False propositions have a truth value of False (F).
• Compound propositions are formed by combining one or more propositions using logical operators.

Types of Compound Propositions

• Negation
• Conjunction
• Disjunction (inclusive or)
• Disjunction (exclusive or)
• Conditional statements
• Biconditional statements

Negation

• The negation of p, denoted by $¬p$ (or $∼p$), is read as