Discrete Math Review Flashcards
is a branch of mathematics that
assumes only distinct separated values.
DISCRETE MATHEMATICS
WHY DO WE NEED TO STUDY DISCRETE MATH?
Mathematical language of computer science
Develops mathematical reasoning by learning
propositional logic and different method of proof
▪ Gateway to more advanced courses in all parts of
mathematical science
or the building up of
machines made up of
electronic devices that
behave logically through
Boolean operations is
based on logic.
HARDWARE
side, database management
systems, programming
languages and artificial
intelligence are based on logic.
SOFTWARE
is the study of reasoning.
It focuses on the relationship among statements and not on the content of the statements.
Its building blocks are called propositions.
LOGIC
are propositions that are assumed
to be true.
AXIOMS
are statements used to
create new concepts in terms of existing ones
DEFINITIONS
is a proposition that has been
proven to be true.
THEOREM
is a theorem that is useful in
proving another theorem
LEMMA
It is a statement that
follows with little or no proof required from an
already proven statement
COROLLARY
is a sequence of statements. The
statements are arguments that establishes the
truth value of a proposition
PROOF
A number is equal to itself
REFLEXIVE AXIOMS
follows Euclid’s Common Notion
One: “Things equal to the same thing are equal to each
other.
Axiom of Equality
which states that every polynomial equation over the field
of complex numbers of degree higher than 1 has a
complex solution or using a formula: P(x) = anxn + … +
a1x + a0 = 0
FUNDAMENTAL THEOREM OF ALGEBRA
is a declarative sentence that is either true or false but not both. The area of logic that deals with this is called the propositional logic.
PROPOSITION
is a tool for the analysis of proof. The truth or falsehood of a proposition is called its
truth value.
LOGIC
can only have two
truth values.
TRUTH VALUE
Propositions, the truth value of which cannot be immediately determined is a
PROPOSITIONAL FUNCTION.
stand for (and can be replaced by) elements from
their DOMAIN.
Variables
The domain is often denoted by
U (the UNIVERSAL).
are formed from existing propositions
using logical operators.
COMPOUND PROPOSITIONS
Logical multiplication/AND operation.
All propositions must
be true so that the
compound proposition
to be TRUE
CONJUNCTION ^
Logical addition /OR operation
Only one true value is
needed to make the
compound proposition
TRUE
DISJUNCTION v
not operation / inversion
Operator reverses the
truth value of the
proposition
NEGATION ¬
a diagram in rows
and columns showing how the truth or falsity of a proposition varies with that of its components.
TRUTH TABLE
proposition p is
called the
antecedent or
hypothesis
proposition q is
called the
consequent or
conclusion
CONVERSE
if q, then p
q → p
proposition p is
called the
antecedent or
hypothesis
proposition q is
called the
consequent or
conclusion
CONTRAPOSITIVE
If not q, then not p
¬q → ¬p
p if and only if q
p is equivalent to q
BI-CONDITIONAL
also
known as deductive logic or
logical deduction is the process of
reasoning from one or more statements
(premises) to reach a logically certain
conclusion.
DEDUCTIVE REASONING,
Puzzles that can be solved using
logical deduction are LOGIC
PUZZLES also known as
QUIZZLES
is one in which the present state of the combination of the logic inputs decides the output
COMBINATIONAL LOGIC CIRCUIT
comprises of input, logic gates and
output variables.
COMBINATIONAL CIRCUIT
means combining two or more logic gates to form a required function where the output at a given time depends only on the input.
COMBINATIONAL LOGIC
keystone of modern electronics. HEART and
BRAINS of most circuits.
INTEGRATED CIRCUIT (IC)
are fundamental building blocks of a combinational circuit.
are electronic circuits that
implement the basic functions of
Boolean Algebra.
LOGIC GATES
is a symbol with two possible
values 0 and 1. can be used to
represent truth values either true or false.
BIT
Information is usually represented
using ___________ which
are lists of zeroes and ones. It is series of zero or more bits.
BIT STRING
is the number of bits in the string.
LENGTH OF THE STRING
is a branch of algebra in which the
values of the variables are
truth values usually denoted 0 and
1.
It is used to analyze and
simplify the digital (logic) circuits.
BOOLEAN ALGEBRA
It was named after (BOOLEAN ALGEBRA)
GEORGE BOOLE
adapted by (BOOLEAN ALGEBRA)
CLAUDE SHANON
are found in computer, cell phones, cars, televisions, wrist watches and other devices.
DIGITAL CIRCUITS
are used to implement digital circuits.
LOGIC GATES
represent logical values. Because of
this, it’s possible to combine the
basic building blocks of a digital
circuit using just the rules of logic.
DIGITAL CIRCUITS
This forms
the algebraic expression showing the operation
of the logic circuit
BOOLEAN ALGEBRA.
This forms the table showing the operation of the logic
circuit
TRUTH TABLE.
This is a graphical representation of a logic circuit that shows the wiring and connections of each individual logic gate,
LOGIC DIAGRAM.
It is a table representation but gives more information than a table.
K-MAP
