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Discrete Mathematics > Discrete Math Review > Flashcards

Discrete Math Review Flashcards

1
Q

is a branch of mathematics that
assumes only distinct separated values.

A

DISCRETE MATHEMATICS

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2
Q

WHY DO WE NEED TO STUDY DISCRETE MATH?

A

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

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3
Q

or the building up of
machines made up of
electronic devices that
behave logically through
Boolean operations is
based on logic.

A

HARDWARE

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4
Q

side, database management
systems, programming
languages and artificial
intelligence are based on logic.

A

SOFTWARE

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5
Q

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.

A

LOGIC

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6
Q

are propositions that are assumed
to be true.

A

AXIOMS

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7
Q

are statements used to
create new concepts in terms of existing ones

A

DEFINITIONS

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8
Q

is a proposition that has been
proven to be true.

A

THEOREM

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9
Q

is a theorem that is useful in
proving another theorem

A

LEMMA

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10
Q

It is a statement that
follows with little or no proof required from an
already proven statement

A

COROLLARY

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11
Q

is a sequence of statements. The
statements are arguments that establishes the
truth value of a proposition

A

PROOF

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12
Q

A number is equal to itself

A

REFLEXIVE AXIOMS

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13
Q

follows Euclid’s Common Notion
One: “Things equal to the same thing are equal to each
other.

A

Axiom of Equality

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14
Q

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

A

FUNDAMENTAL THEOREM OF ALGEBRA

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15
Q

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.

A

PROPOSITION

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16
Q

is a tool for the analysis of proof. The truth or falsehood of a proposition is called its
truth value.

A

LOGIC

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17
Q

can only have two
truth values.

A

TRUTH VALUE

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18
Q

Propositions, the truth value of which cannot be immediately determined is a

A

PROPOSITIONAL FUNCTION.

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19
Q

stand for (and can be replaced by) elements from
their DOMAIN.

A

Variables

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20
Q

The domain is often denoted by

A

U (the UNIVERSAL).

21
Q

are formed from existing propositions
using logical operators.

A

COMPOUND PROPOSITIONS

22
Q

Logical multiplication/AND operation.

All propositions must
be true so that the
compound proposition
to be TRUE

A

CONJUNCTION ^

23
Q

Logical addition /OR operation

Only one true value is
needed to make the
compound proposition
TRUE

A

DISJUNCTION v

24
Q

not operation / inversion

Operator reverses the
truth value of the
proposition

A

NEGATION ¬

25
Q

a diagram in rows
and columns showing how the truth or falsity of a proposition varies with that of its components.

A

TRUTH TABLE

26
Q

proposition p is
called the
antecedent or
hypothesis

proposition q is
called the
consequent or
conclusion

A

CONVERSE

if q, then p

q → p

27
Q

proposition p is
called the
antecedent or
hypothesis

proposition q is
called the
consequent or
conclusion

A

CONTRAPOSITIVE

If not q, then not p

¬q → ¬p

28
Q

p if and only if q
p is equivalent to q

A

BI-CONDITIONAL

29
Q

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.

A

DEDUCTIVE REASONING,

30
Q

Puzzles that can be solved using
logical deduction are LOGIC
PUZZLES also known as

A

QUIZZLES

31
Q

is one in which the present state of the combination of the logic inputs decides the output

A

COMBINATIONAL LOGIC CIRCUIT

32
Q

comprises of input, logic gates and
output variables.

A

COMBINATIONAL CIRCUIT

33
Q

means combining two or more logic gates to form a required function where the output at a given time depends only on the input.

A

COMBINATIONAL LOGIC

34
Q

keystone of modern electronics. HEART and
BRAINS of most circuits.

A

INTEGRATED CIRCUIT (IC)

35
Q

are fundamental building blocks of a combinational circuit.

are electronic circuits that
implement the basic functions of
Boolean Algebra.

A

LOGIC GATES

36
Q

is a symbol with two possible
values 0 and 1. can be used to
represent truth values either true or false.

A

BIT

37
Q

Information is usually represented
using ___________ which
are lists of zeroes and ones. It is series of zero or more bits.

A

BIT STRING

38
Q

is the number of bits in the string.

A

LENGTH OF THE STRING

39
Q

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.

A

BOOLEAN ALGEBRA

40
Q

It was named after (BOOLEAN ALGEBRA)

A

GEORGE BOOLE

41
Q

adapted by (BOOLEAN ALGEBRA)

A

CLAUDE SHANON

42
Q

are found in computer, cell phones, cars, televisions, wrist watches and other devices.

A

DIGITAL CIRCUITS

43
Q

are used to implement digital circuits.

A

LOGIC GATES

44
Q

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.

A

DIGITAL CIRCUITS

45
Q

This forms
the algebraic expression showing the operation
of the logic circuit

A

BOOLEAN ALGEBRA.

46
Q

This forms the table showing the operation of the logic
circuit

A

TRUTH TABLE.

47
Q

This is a graphical representation of a logic circuit that shows the wiring and connections of each individual logic gate,

A

LOGIC DIAGRAM.

48
Q

It is a table representation but gives more information than a table.

A

K-MAP

Discrete Mathematics (1 decks)

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