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33 Cards in this Set
- Front
- Back
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Statement |
declarative sentences that are either true or false, but not both simultaneously |
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Compound statement |
combines two or more statements |
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connectors |
include: and, or, if...then |
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Negation |
must have the opposite truth value from the original statement |
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Negation of symbols < and > |
<=>or equal to >=<or equal to |
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^ |
and, conjunction |
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\/ |
or, disjunction |
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~ |
not, negation |
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Quantifiers |
used to determine how many cases of a particular situation exists. There are universal quantifiers and existential quantifiers |
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Universal quantifiers |
all, each, every, none |
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Existential quantifiers |
some, there exists, for atleast |
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Negating quantifiers |
the negation of an existential quantifier is a universal quantifier, while the negation of a universal quantifier is a existential quantifier |
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Truth Table |
the listing of all possible truth values of a statement |
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Basic Truth table for p and q |
(p^q) is only true when they are both true |
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Basic truth table for p or q |
(p\/q) is only false when they are both false |
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Negation of a statement p |
~p must have opposite truth value of the original statement |
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How do we determine the number of rows in a truth table? |
n symbols, want 2^n rows |
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Equivilent statements( |
Have the same truth value in all possible situations |
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DeMorgan's Law |
~(p\/q) equivilent to (~p^~q) ~(p^q) equivilent to (~p\/~q) |
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Circuits |
They are analogous to logical statements w/ parallel circuits corresponding to disjunctions and series circuits corresponding to conjunctions |
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DeMorgan's 2nd law |
p->q equivillent to ~p\/q |
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conditional statement |
uses if...then connective and is symbolized by p-->q where p is the antecendent and q is the consequent |
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what is the equivilent of a conditional statement |
a disjunction: ~p\/q |
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what is the negation of a conditional statement |
a conjunction: p^~q |
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What is the converse of a conditional statement? |
q-->p |
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What is the inverse of a conditional statement? |
~P-->~q |
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What is the contrapositive of a conditional statement? |
~q-->~p |
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What is the negation of a conditional statement? |
p^~q |
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What are the 2 equivilences among those 5 statements? |
original is equivilent to the contrapositive converse is equivilent to the inverse |
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Biconditional statement |
p<-->q, p if and only if q. both must have the same truth value |
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Logical argument |
a series of statements with each statement being a premise and the last one being the conclusion |
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When is a statement valid? |
if all the premises are true, this forces the conclusion to follow and it is valid, otherwise it is invalid |
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What are the 2 ways we can analyze for validity? |
Euler diagram and truth tables. |
