Discrete Test 1
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Created by:
AnAngrySpring on January 26, 2012
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41 terms
Terms | Definitions |
|---|---|
 Subset | A⊆B, "A is a subset of B" means ∀x(x∈A=>x∈B) a set whose members are members of another set If A is not a subset of B: A⊄B |
| Proper subset | If A⊆B, but A≠B (meaning there is something in B which is not in A) A subset that does not contain every element in another set. |
| Relative complement | The complement of A relative to B, written B - A is the set of all elements in B that are not in A. |
| Cartesian Product | the set of elements common to two or more sets |
| Propositional function | a statement containing one or more variables that becomes a propositions when each of its variables is assigned a value or is bound by a quantifier |
| Universal quantification | "P(x) is true for all values x in the universe of discourse." AxP(x) |
| Existential quanti cation | "There exists an element x in the universe of discourse such that P(x) is true." ExP(x) |
| proposition | is a declarative sentence that is either true (denoted either T or 1) or false (denoted either F or 0). |
| conjunction | "p and q", p ^ q |
| disjunction | "p or q", p V q |
| exclusive or | "exactly one of p or q", \p xor q", p (+) q |
| implication | "if p then q", p --> q |
| biconditional | "P if and only if q", p <--> q. |
| P ^ Q | only T if both P and Q are T |
| P V Q | only F is both P and Q are F |
| p (+) q | Only F when p and q are the same answer |
| p --> q | Only false if p is T and q is F |
| converse | switch p and q |
| inverse | ~p --> ~q |
| contrapositive | ~q --> ~p |
| p <--> q | Only true when both p and q are the same |
| p|q | Only F if p and q are T |
| p(down arrow)q | Only T if p and q are F |
| Image | x |
| pre-image | y |
| xA(s) = 1 if | s is a member of A |
| tautology | proposition that is always true pV~p |
| contradiction | always false p ^ ~p |
| contingency | neither a tautology nor a contradiction |
| logically equivalent | if r <-->s is a tautology |
| Identity Laws | (p ^ T = p) (p ^ F = F) (p V T = T) (p V F = p) |
| Domination Laws | P ∨ T ≡ T P ∧ F ≡ F |
| Idempotent Laws | P ∨ P ≡ P P ∧ P ≡ P |
| Double Negation Law | ¬(¬P) ≡ P |
| Commutative Laws | P ∨ Q ⇔ Q ∨ P P ∧ Q ⇔ Q ∧ P |
| Associative Laws | (P ∨ Q) ∨ R ≡ P ∨ (Q ∨ R) (P ∧ Q) ∧ R ≡ P ∧ (Q ∧ R) |
| Distributive Laws | p∨(q∧r) ≡ (p∨q)∧(p∨r) p∧(q∨r) ≡ (p∧q)∨(p∧r)) |
| De Morgan's Laws | ~ (P and Q) = ~ P or ~ Q ~ (P or Q) = ~ P and ~ Q |
| Absorption Laws | P ∨ ( P ∧ Q ) ⇔ P P ∧ ( P ∨ Q ) ⇔ P |
| Implication Law | (P --> Q) ⇔ (~P ∨ Q) |
| unique existential quanti cation | "There exists a unique element x in the universe of discourse such that P(x) is true." E!xP(x) |
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