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Cards (330)
Invertible
function
A→B is invertible iff
bijective
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Invertible
functions is a
function f that has an
inverse
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Sequence
A function whose
domain
is a subset of ℕ
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Geometric sequence
a type of sequence where each succeeding term is produced by multiplying each preceding term by a
fixed number
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Recurrence
relation
An equation that expresses aₙ in terms of earlier terms: aₙ₋₁, aₙ₋₂, ...
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Closed formula
A function of n that satisfies the
recurrence relation
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Summation (or series)
is the
sum of a sequence
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A way to define a sequence of numbers or values by providing a formula that specifies how the next term is related to previous terms
A
recurrence relation
Proposition
A statement that can be
assigned a truth value (True or False)
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Propositionsexamples
It is raining today
2+3=5
2+3=7
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Negation (not)
The negation of a proposition P is
'not P'
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Conjunction
'P and Q'
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Disjunction (or, inclusive or)
The
disjunction of propositions
P and Q is
'P or Q'
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Exclusive or
The
exclusive or of propositions
P and Q is
'P or Q
, but not
both'
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Implication (if-then)
The implication of P to Q is 'if P, then Q'
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Biconditional (if and only if)
The biconditional of P and Q is
'P if and only if Q'
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Atomic Proposition
A
basic proposition
that
cannot be broken down
further
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Compound Proposition
A
proposition
built from
atomic
propositions and
logical
operations
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P → (Q > R) is a
meaningful compound proposition
, but P → Q → R is
meaningless
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Tautology
A
compound proposition
that is
true
for
every assignment
of
truth values
to its
propositional variables
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Contradiction
A
compound proposition
that is
false
for every assignment of
truth values
to its
propositional
variables
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Satisfiable
A
proposition that is not a contradiction
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Contingency
A proposition that is
neither a tautology
nor a
contradiction
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Logically Equivalent
Two propositions A and B are logically equivalent if A↔B is a tautology
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P→Q =
¬P∨Q
(
implication is equivalent to disjunction of negation
and
consequent
)
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P→Q
=
¬Q→¬P
(implication is equivalent to the contrapositive)
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P→Q ≠ ¬P→P (the
inverse
of an implication is
not equivalent
)
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P↔Q = (
P→Q
)∧(
Q→P
) (
biconditional
is equivalent to the
conjunction
of
two implications
)
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P
9 unless
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Equivalences
1.3
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Tautology
A
compound Prop.
that is
true
for
every assignment
of
truth Values
to its
Propositional Variables
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Contradiction
A
compound Prop. that is false for every assignment
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Tautology
P v ~P
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Contradiction
P ^ ~P
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P
-> (
P v q
) is a
tautology
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Contingency
A prop. that is
neither a tautology
nor a
contradiction
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Logically equivalent
Two Propositions A,B are said to be logically equivalent iff A&B is a tautology
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Notation
:
A = B
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A
=
B
iff
A&B
have the same
truth table
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Logically equivalent
P
->
q
= ~
P v q
P
=>
q
= ~
P
v q
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