Logic Flashcards
discipline that deals with the methods of reasoning
Logic
provides rules and techniques for determining whether a given argument
is valid.
Logic
earlier names for mathematical logic
Symbolic logic and metamathematics
method of representing logical expressions through the use of symbols
and variables, rather than ordinary
Logic
declarative sentence that is either true or false but not both.
Proposition
arbitrary representation and it is commonly
represented by letters p. q, and r
Propositional variables
the property of a statement being either true or false
Truth value
a combination of two or more simple
propositions.
Compound propositions
use to join or combine two or more
statements to form a new statement. Usually written as a
symbol that carries particular instruction of how to operate a
statement or compound statement
Logical connective
provides the truth value for the result of applying
operand on each possible set of truth values for the operands
Truth table
indicates the opposite; the symbol resembles a
dash with a tail (¬),
arithmetic subtraction
symbol (-), or a tilde (~ ).
Negation
a compound sentence formed
by the word AND to join two
simple sentences
Conjunction
the symbol ampersand (&) used
to signify this. Other
common symbols are a dot and
an upside down wedge (∧ ).
Conjunction
a compound sentence formed
by the word OR to join two
simple sentences
Disjunction
uses symbol called vel ( ∨ )
Disjunction
logical operation exclusive
disjunction.
Symbolized as XOR, EOR,
EXOR, or direct sum, ⨁ (circled
plus)
Exclusive-Or
logical operation exclusive
disjunction.
Symbolized as XOR, EOR,
EXOR, or direct sum, ⨁ (circled
plus)
Exclusive-Or
represents the inequality
function.
Exclusive-Or
connective equivalent to the
composition of NOT AND; referred to as alternative
denial
NAND
Notations used are ~ ∧ , ↑ (up
arrow) also known as sheffer
stroke
NAND
a connective equivalent to the
composition of NOT OR
Also referred to as joint denial
NOR
symbol used are ∽ ⋁, ↓ (down
arrow), also known as Quine
arrow.
NOR
The statement “ïf p then q” is called ________
implication or conditional
The statement “p if and only if q” is
called
biimplication or
biconditional (of p and q)
Also known as logical equality
Biconditional statement
Example: “If it is noon, then I am hungry.”
“If I am hungry, then it is noon.”
Converse
“If it is noon, then I am hungry.”
“If it is not noon, then I am not hungry.”
Inverse
“If it is noon, then I am hungry.”
“If I am not hungry, then it is not noon.”
Contrapositive
Find the converse, inverse and contrapositive of the statement,
“If the train is late then the bus is full“
Converse: “If the bus is full then the train is late”
Inverse: “If the train is not late then the bus is not full”
Contrapositive: “If the bus is not full then the train is not late”
a type of relationship between
two statements or sentences in propositional logic
with identical truth table(s).
Logical equivalence
refers to the proposition
that is TRUE for all
possible values of its
propositional variables
Tautology
refers to the proposition
that is FALSE for all
possible values of its
propositional variables.; also known as absurdity
Contradiction
refers to the statement
that can either be TRUE
or FALSE, depending on
the truth values of its
propositional variables
Contigency
consists of a set of premises and a conclusion.
Symbolic arguments
what does the symbol ∴ denotes
Conclusion
When is an argument valid
when its conclusion necessarily
follows from a given set of premises; ALL must be true
When is an argument invalid or a fallacy
when the conclusion
does not necessarily follow from the given set of
premises
Rule for Conjunction
Proposition is defined to be TRUE only
when both p and q are true, and false
otherwise
Rule for Disjunction
Proposition is defined to be FALSE only
when both p and q are false, and true
otherwise
Rule for Exclusive-Or
Proposition is defined to be TRUE when
exactly one of p and q is true, and false
otherwise.
Rule for NAND
Proposition that is TRUE when either p
and q, or both are false; and is is false when p
and q are true
Rule for NOR
Proposition that is TRUE when both p
and q are false, and it is false otherwise.
Rule for conditional statement
Proposition that is TRUE for all input
values except when true implies false
Biconditional statement
Proposition that is TRUE when both p
and q are either true or false, or else the
result is FALSE
