A compiled <li> of information!

Finally got around to updating my glossary as I was working on the thing. It's relatively useless since we have course notes, but I think it's a pretty comprehensive list.

I'll track the changes I make today under the 'read more' or whatever you want to call it here.

Glossary as of Post-Creation (Haha.):
Symbols     For a complete list, see Wikipedia's List of Logic Symbols.
⇒ - Implication: "P(x) ⇒ Q(x)" means "If P(x) then Q(x)".
⇔ - Bi-implication: "P(x) ⇔ Q(x)" means "If P(x) then Q(x)" and "If Q(x) then P(x)". Also applies for iff statements ("P(x) if and only if Q(x)")
¬ - Toggle: "¬P(x)" means "Not P(x)".
∧ - And: "P(x) ∧ Q(x)" means "P(x) and Q(x)".
∨ - Or: "P(x) ∨ Q(x)" means "P(x) or Q(x)".
∀ - Universal Claim: Generally means "For all" or "Every".
∃ - Existential Claim: Generally means "There exists" or "Some".
∪ - Union: The combination of two sets (ex. "P ∪ Q" is essentially a set with all of the elements in P, and all of the elements in Q.)
∩ - Intersection: The common set between two other sets (ex. "P ∩ Q" is essentially a set containing the elements that appear in both P and Q.)
∈ - Element: Generally used to show that an item is in a set.
≡ - Equivalence: Indicates that two sides are exactly the same.

Keywords

• "Antecedent" - In "P(x) ⇒ Q(x)" it is the "P(x)".
• "Consequent" - In "P(x) ⇒ Q(x)" it is the "Q(x)".
• "Converse" - "P(x) ⇒ Q(x)" ⇔ "Q(x) ⇒ P(x)"; Switch the order of implication.
• "Contrapositive" - "P(x) ⇒ Q(x)" ⇔ "¬Q(x) ⇒ ¬P(x)"; Toggle each side and switch the order of implication. This yields the same truth table as the original statement.
• "Yet" or "But" - Both mean "And", just with a different connotation.
• "Unless" → "If not"

Negation

• "P(x) ⇒ Q(x)" ⇔ "P(x) ∧ ¬Q(x)"
• "∀x∈Y..." ⇔ "∃x∈Y..."
• "∧" ⇔ "∨"
• "P(x) ∧ Q(x)" ⇔ "¬P(x) ∨ ¬Q(x)"

Identities and Properties

• "(P ∧ Q) ∧ R" ≡ "P ∧ (Q ∧ R)" - Associative - "(P ∨ Q) ∨ R" ≡ "P ∨ (Q ∨ R)"
• "(P ∧ (Q ∨ R)" ≡ "(P ∧ Q) ∨ (P ∧ R)" - Distributive - "(P ∨ (Q ∧ R)" ≡ "(P ∨ Q) ∧ (P ∨ R)"
• "P ∧ (Q ∨ ¬Q)" ≡ P ≡ "P ∨ (Q ∧ ¬Q)"
• "P(x) ⇒ Q(x)" ≡ "¬Q(x) ⇒ ¬P(x)" - This is also the contrapositive.

Changes to Key Terms (19:56 01/28/2013):

• "Conjunction" - The connection of two statements through the use of "And". (Ex. "The conjunction of P and Q" ≡ "P ∧ Q")
• "Disjunction" - The separation of two statements through the use of "Or". (Ex. "The disjunction of P and Q" ≡ "P ∨ Q")

Minor Changes (18:56 01/30/2013):

• Minor fixes to existing statements.
• References Page 29.
• Added identities: "P ⇒ Q" ≡ "¬P ∨ Q" and "(P ⇒ R) ∧ (Q ⇒ R)" ≡ "P ∨ Q ⇒ R"