Discrete Math

Question 1

Individually separate and distinct.

Answer 1

discrete

Question 2

(thetheory of ways things combine; in particular, how to count these ways)

Answer 2

combinatorics

Question 3

is any declarative sentence which is either true or false.

Answer 3

statement

Question 4

__________is atomic if it cannot be divided into smaller statements, otherwise it is _________

Answer 4

statement, molecular

Question 5

You can build more complicated (molecular) statements out of simpler ones using ________

Answer 5

logical connectives.

Question 6

Logical connectives are called _________ when they connecttwo statements while a ____________ applies to a single statement.

Answer 6

binary connectives, unary connective

Question 7

(sometimes called sentential variables), usually capital lettersin the middle of the alphabet: P, Q, R, S, . . ..

Answer 7

propositional variables

Question 8

A composite proposition, in which is composed of sub propositions andvarious connectives is referred to as a __________

Answer 8

compound proposition.

Question 9

A proposition is said to be ________ if it cannot be broken downinto simpler propositions, that is, if it is not composite.

Answer 9

primitive

Question 10

P ∧ Q is read “P and Q,” and called a ____________

Answer 10

conjunction.

Question 11

P ∨ Q is read “P or Q,” and called a ________

Answer 11

disjunction.

Question 12

P → Q is read “if P then Q,” and called an ________

Answer 12

implication or conditional.

Question 13

P ↔ Q is read “P if and only if Q,” and called a ________

Answer 13

biconditional.

Question 14

¬P is read “not P,” and called a

Answer 14

negation

Question 15

We say that P is the ________ (or antecedent), and Q is the _________ (or consequent).

Answer 15

hypothesis, conclusion

Question 16

is the study of consequence.

Answer 16

logic

Question 17

An ________ is a set of statements, one of which is called the_________ and the rest of which are called _________.

Answer 17

argument, conclusion, premises

Question 18

An argument which is not valid is called a ________

Answer 18

fallacy.

Question 19

is simply a statement.

Answer 19

proposition

Question 20

studies the ways statements can interact with eachother.

Answer 20

Propositional logic

Question 21

The _________ of a compound propositions is referred to as exclusive disjunction.

Answer 21

exclusive or

Question 22

A variable is called a _____________ if its value is either true or
false.

Answer 22

Boolean variable

Question 23

is a sequence of zero or more bits.

Answer 23

bit string

Question 24

is a mathematical expression that has a variable as its subject, and a predicate which is the property the
variable. It is denoted by P(x).

Answer 24

propositional function

Question 25

is a proposition whose truth depends on the value of one or more variables.

Answer 25

predicate

Question 26

expresses the extent to which a predicate is true over a range of elements.

Answer 26

Quantification

Question 27

of P (x) for a particular domain is the proposition that asserts that P (x) is true for all values of x in this domain.

Answer 27

universal quantification

Question 28

The symbol ∃ which reads “there exists” or “for some” or “for at least one” is called the

Answer 28

existential quantifier.

Question 29

we form a proposition that is true if and only if P (x) is true for at least one value of x in the domain.

Answer 29

existential quantification,

Question 30

is a statement which is true on the basis of its logical form alone.

Answer 30

tautology

Question 31

if it is false for any truth values of its variables.

Answer 31

contradiction

Question 32

A compound proposition that is neither a tautology nor a contradiction is a

Answer 32

contingency.

Question 33

Two (molecular) statements P and Q are ______________ provided P is true precisely when Q is true.

Answer 33

logically equivalent

Question 34

The way to distribute a negation over a disjunction (an or) has a similar rule for distributing over a conjunction (and).

Answer 34

De Morgan’s Law

Question 35

To write this statement symbolically, we must use

Answer 35

quantifiers.

Question 36

Better to think of P and O as denoting properties of their input. The technical term for these is _________ and when we study them in logic, we need to use _________.

Answer 36

predicates, predicate logic