LOGIC

• These are letters to denote propositions.

  Propositional Variables
• Between true (T) or false (F), what is the equivalent of 1?

  True
• Between true (T) or false (F), what is the equivalent of 0?

  False
• This is a declarative sentence that is either TRUE or FALSE.

  Proposition
• What is NOT true about Propositions?

  a.) It is not both TRUE and FALSE at the same time.

  b.) It can be both TRUE and FALSE at the same time.

  c.) It is not neither TRUE nor FALSE.

  d.) It is not 50% TRUE and 50% FALSE.

  B.
• These are used to form compound propositions.

  Operators
• What operator does the symbols ~ or ¬ refer to?

  Negation
• What operator does the symbol ∧ refer to?

  Conjunction
• What operator does the symbol ∨ refer to?

  Disjunction
• What operator does the symbol ⊕ refer to?

  Exlusive-OR
• It indicates the opposite of the statement --- "It is not the case that..."

  Negation
• It is a compound statement formed by the word AND to join two simple propositions.

  Conjunction
• It is a compound statement formed by the word OR to join two simple propositions.

  Disjunction
• It refers to a logical operation exclusive disjunction.

  Exclusive-OR
• What operator does the symbol ⇒ or → refer to?

  Conditional / Implication
• What operator does the symbol ⇐⇒ refer to?

  Biconditional
• T | F

  F | T

  Negation
• T | T | T

  T | F | F

  F | T | F

  F | F | F

  Conjunction
• T | T | T

  T | F | T

  F | T | T

  F | F | F

  Disjunction
• T | T | F

  T | F | T

  F | T | T

  F | F | F

  Exclusive-OR
• T | T | T

  T | F | F

  F | T | T

  F | F | T

  Conditional / Implication
• T | T | T

  T | F | F

  F | T | F

  F | F | T

  Biconditional
• This refers to combination of one or more propositions using logical connectives or operators.

  Compound Propositions
• Between p and q, the hypothesis _ is also called the sufficient condition, premise, or antecedent.

  p
• Between p and q, the hypothesis _ is also called the necessary condition or the consequence.

  q
• This means always TRUE logical expression.

  Tautology
• This means always FALSE logical expression.

  Contradiction / Fallacy
• This means the logical expression is neither true or false.

  Contingency
• p → q

  Given / Direct
• ~q → ~p

  Contrapositive
• ~p → ~q

  Inverse
• q → p

  Converse
• What law does the following logical equivalence refer to?

  p v F ≡ p

  p ∧ T ≡ p

  Identity
• What law does the following logical equivalence refer to?

  p ∨ T ≡ T

  p ∧ F ≡ F

  Domination
• What law does the following logical equivalence refer to?

  p ∨ p ≡ p

  p ∧ p ≡ p

  Idempotent
• What law does the following logical equivalence refer to?

  ~(~p) ≡ p

  Double Negation
• What law does the following logical equivalence refer to?

  p ∨ q ≡ q ∨ p

  p ∧ q ≡ q ∧ p

  Commutative
• What law does the following logical equivalence refer to?

  (p ∨ q) ∨ r ≡ p ∨ (q ∨ r)

  (p ∧ q) ∧ r ≡ p ∧ (q ∧ r)

  Associative
• What law does the following logical equivalence refer to?

  p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)

  p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)

  Distributive
• What law does the following logical equivalence refer to?

  ~(p ∨ q) ≡ ~p ∧ ~q

  ~(p ∧ q) ≡ ~p ∨ ~q

  De Morgan's