Help
Options
Didn't know it?
click below
click below
Knew it?
click below
click below
Don't Know
Remaining cards (0)
Know
retry
shuffle
restart
0:00
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.
Normal Size Small Size show me how
Normal Size Small Size show me how
MATH211-Exam1
| Term | Definition |
|---|---|
| (definition) universal statement | Says that a certain property is true for all elements in a set. |
| (definition) conditional statement | Says that if one thing is true then some other thing is also true. |
| (definition) existential statement | Says that there is at least one thing for which some property is true. |
| universal statement form | "For all..." |
| conditional statement form | "If..., then..." |
| existential statement uses form | "There exists..." |
| (definition) universal conditional statement | A statement that is both universal and conditional |
| universal conditional statement form | "For all _____(set), if _____(check property), then _____(property to follow)." |
| (definition) universal existential statement | A statement that is universal because its first part says that a certain property is true for all objects of a given type, and it is existential because its second part asserts the existence of something. |
| universal existential statement form | "For all _____(set), there is _____(property/object specific)." |
| (definition) existential universal statement | A statement that is existential because its first part asserts that a certain object exists and is universal because its second part says that the object satisfies a certain property for all things of a certain kind. |
| existential universal statement form | "There exists _____(object in set), such that for all _____(set), _____(property)." |
| (definition) logic | The study of reasoning; it is specifically concerned with whether reasoning is correct. |
| (definition) argument | A sequence of statements aimed at demonstrating the truth of an assertion. |
| conclusion | The assertion at the end. |
| premises | Statements leading to an assertion. |
| (definition) statement/proposition | A sentence that is true or false but not both. The truth value is TRUE if it is true and FALSE if it is false. |
| negation of p | Means "not p" or "it is not that case that p" |
| negation of p denotion | ~p |
| the conjunction of p and q | Means "p and q" |
| the conjunction of p and q denoted | p ∧ q |
| the disjunction of p and q | Means "p or q" |
| the disjunction of p and q denoted | p ∨ q |
| (definition) logical equivalence | Statement forms that have identical truth values for each possible substitution for their statement variables. |
| logical equivalence denoted | P≡Q |
| De Morgan's Laws (a) | ~(p ∧ q) ≡ ~p ∨ ~q |
| De Morgan's Laws (b) | ~(p ∨ q) ≡ ~p ∧ ~q |
| (definition) tautology | A statement that is always true. |
| (definition) contradiction | A statement that is always false. |
| (definition) conditional statements | "if p then q" |
| conditional statements denoted | p --> q (p is the hypothesis, q is the conclusion) |
| (definition) vacuously true | A conditional statement that is true by virtue of the fact that its hypothesis is false. |
| (theorem) p → q ≡∼ p∨q | (theorem) The statement “if p then q” is logically equivalent to “not p or q.” |
| (theorem) ~(p → q) ≡ p ∧ ~q | (theorem) The negation of “if p then q” is logically equivalent to “p and not q”. |
| (definition) contrapositive of p --> q | ~q --> ~p |
| (theorem) p --> q ≡ ~q --> ~p | (theorem) A conditional statement is logically equivalent to its contrapositive. |
| (definition) converse of p --> q | q --> p |
| (definition) inverse of p --> q | ~p --> ~q |
| (definition) "p only if q" means... | "if not q then not p." / "if p then q" |
| Order of operations for logical operators | 1. ~ [negations first] 2. ∧, ∨ [evaluate ∧ ∨ second, parentheses may be needed] 3. -->, <--> [evaluate -> and <--> third, parentheses may be needed] |
| (definition) sufficient condition | If r and s are statements: r is a sufficient condition for s means “if r then s.” r is a necessary condition for s means “if not r then not s” or “if s then r.” |
| (definition) syllogism | An argument form with two premises and a conclusion. |
| modus ponens | p-->q p ∴q |
| modus tollens | p-->q ~q ∴~p |
| rule of inference | A form of argument that is valid. |
| generalization | A valid argument form. p ∴ p∨q q ∴ p∨q |
| specialization | A valid argument form. |
| elimination | p ∨ q ~q ∴ p p ∨ q ~p ∴ q |
| transitivity | p --> q q --> r ∴ p --> r |
| Proof by Division into Cases | p ∨ q p --> r q --> r ∴ r |
| Contradiction Rule | If you can show that the assumption that statement p is false leads logically to a contradiction, then you can conclude that p is true. ~p --> c ∴ p |
| (definition) fallacy | An error in reasoning that results in an invalid argument. |
| converse error | An invalid argument form. p --> q q ∴ p |
| inverse error | An invalid argument form p-->q ~p ∴ ~q |
| (definition) predicate | A sentence that contains a finite number of variables and becomes a statement when specific values are substituted for the variables. |
| (definition) domain | The set of all values that may be substituted in place of the predicate variable |
| Method of Exhaustion | When a domain is finite, a technique for showing that a universal statement is true. |
| (definition) existential statement | A statement of the form “There is an x in the domain such that Q(x)." It is defined to be true if, and only if, Q(x) is true for at least one x in D. It is false if, and only if, Q(x) is false for all x in D. |
| universal conditional statement | "For all of x, if P(x) then Q(x)." |
| (theorem) Negation of a Universal Statement | "For all x in D, Q(x) is true" to "There exists an x in D such that Q(x) is not true." |
| (theorem) Negation of an Existential Statement | "There exists an x in D such that Q(x) is true." to "For all x in D, Q(x) is false." |
| (theorem) Negation of a Universal Conditional Statement | "For all of x, if P(x) then Q(x)." to "There exists an x such that P(x) and ~Q(x)." |
| Sufficient condition for "For all of x, if r(x) then s(x)." | "For all of x in r(x)." |
| Necessary condition for " ~if r(x) then ~s(x)." | "For all of x in r(x)." |
| Only if for "~s(x) then ~r(x)." | "For all of x in r(x)." |
| Rule of Universal Instantiation | If some property is true of everything in a domain, then it is true of any particular thing in the domain. |
| Universal Modus Ponens | (Universal Instantiation) ∀x, if P(x) then Q(x) [<--major premise] P(a) for a particular a [<-- minor premise] ∴ Q(a) |
| Universal Modus Tollens | ∀x, if P(x) then Q(x) ~ Q(a) for a particular a ∴ ~P(a) |
| Universal Transitivity | ∀x, P(x) --> Q(x) ∀x, Q(x) --> R(x) ∴ ∀x, P(x) --> R(x) |
| Converse Error | ∀x, if P(x) then Q(x) Q(a) for a particular a ∴ P(a) |
| Inverse Error | ∀x, P(x) --> Q(x) ~P(a) for a particular a ∴ ~Q(a) |
Created by:
user-1737194
Popular Math sets