Discrete Math Review

Question 1

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

Answer 1

DISCRETE MATHEMATICS

Question 2

WHY DO WE NEED TO STUDY DISCRETE MATH?

Answer 2

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

Question 3

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

Answer 3

HARDWARE

Question 4

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

Answer 4

SOFTWARE

Question 5

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.

Answer 5

LOGIC

Question 6

are propositions that are assumed
to be true.

Answer 6

AXIOMS

Question 7

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

Answer 7

DEFINITIONS

Question 8

is a proposition that has been
proven to be true.

Answer 8

THEOREM

Question 9

is a theorem that is useful in
proving another theorem

Answer 9

LEMMA

Question 10

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

Answer 10

COROLLARY

Question 11

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

Answer 11

PROOF

Question 12

A number is equal to itself

Answer 12

REFLEXIVE AXIOMS

Question 13

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

Answer 13

Axiom of Equality

Question 14

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

Answer 14

FUNDAMENTAL THEOREM OF ALGEBRA

Question 15

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.

Answer 15

PROPOSITION

Question 16

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

Answer 16

LOGIC

Question 17

can only have two
truth values.

Answer 17

TRUTH VALUE

Question 18

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

Answer 18

PROPOSITIONAL FUNCTION.

Question 19

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

Answer 19

Variables

Question 20

The domain is often denoted by

Answer 20

U (the UNIVERSAL).

Question 21

are formed from existing propositions
using logical operators.

Answer 21

COMPOUND PROPOSITIONS

Question 22

Logical multiplication/AND operation.

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

Answer 22

CONJUNCTION ^

Question 23

Logical addition /OR operation

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

Answer 23

DISJUNCTION v

Question 24

not operation / inversion

Operator reverses the
truth value of the
proposition

Answer 24

NEGATION ¬

Question 25

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

Answer 25

TRUTH TABLE

Question 26

proposition p is called the antecedent or hypothesis proposition q is called the consequent or conclusion

Answer 26

CONVERSE if q, then p q → p

Question 27

proposition p is called the antecedent or hypothesis proposition q is called the consequent or conclusion

Answer 27

CONTRAPOSITIVE If not q, then not p ¬q → ¬p

Question 28

p if and only if q p is equivalent to q

Answer 28

BI-CONDITIONAL

Question 29

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.

Answer 29

DEDUCTIVE REASONING,

Question 30

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

Answer 30

QUIZZLES

Question 31

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

Answer 31

COMBINATIONAL LOGIC CIRCUIT

Question 32

comprises of input, logic gates and output variables.

Answer 32

COMBINATIONAL CIRCUIT

Question 33

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

Answer 33

COMBINATIONAL LOGIC

Question 34

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

Answer 34

INTEGRATED CIRCUIT (IC)

Question 35

are fundamental building blocks of a combinational circuit. are electronic circuits that implement the basic functions of Boolean Algebra.

Answer 35

LOGIC GATES

Question 36

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

Answer 36

BIT

Question 37

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

Answer 37

BIT STRING

Question 38

is the number of bits in the string.

Answer 38

LENGTH OF THE STRING

Question 39

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.

Answer 39

BOOLEAN ALGEBRA

Question 40

It was named after (BOOLEAN ALGEBRA)

Answer 40

GEORGE BOOLE

Question 41

adapted by (BOOLEAN ALGEBRA)

Answer 41

CLAUDE SHANON

Question 42

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

Answer 42

DIGITAL CIRCUITS

Question 43

are used to implement digital circuits.

Answer 43

LOGIC GATES

Question 44

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.

Answer 44

DIGITAL CIRCUITS

Question 45

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

Answer 45

BOOLEAN ALGEBRA.

Question 46

This forms the table showing the operation of the logic circuit

Answer 46

TRUTH TABLE.

Question 47

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

Answer 47

LOGIC DIAGRAM.

Question 48

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

Answer 48

K-MAP