Propositional Logic

Definition

• Proposition

  • a declarative sentence that can be true or false.
  • often denoted with variables , , or .
  • a proposition has a truth value.
    • it can either be true or false.

• Truth Table

  • it shows all values of a given proposition
  • used to define logical operators
  • used to exhibit relationships between simple components’ thruth values to the compound propositions’ truth values
  • a truth table with propositions has rows.

Types

• Simple
  • conveys a single thought
• Compound
  • two or more propositions
  • put together with connective words

Operator

• Negation: negates/reverses the truth value.

T	F
F	T

• Conjunction (and): true whenever two propositions are true
  • The two propositions and are called conjuncts.

T	T	T
T	F	F
F	T	F
F	F	F

• Disjunction (or)
  • The operands are called disjuncts.

T	T	T
T	F	T
F	T	T
F	F	F

• Conditional
  • is called hypothesis
  • is the conclusion

T	T	T
T	F	F
F	T	T
F	F	T

• Biconditional

T	T	T
T	F	F
F	T	F
F	F	T