Propositions

Question 1

is a declarative sentence (that is, a sentence that declares a fact) that is either
true or false, but not both.

Answer 1

proposition

Question 2

We use letters to denote_____________________, that is, variables
that represent propositions, just as letters are used to denote numerical variables

Answer 2

propositional variables(or sentential variables)

Question 3

The conventional letters used for propositional variables are

Answer 3

p, q, r, s, …

Question 4

a proposition is true, denoted by T, if it is a true proposition, and the truth value of a proposition is false, denoted by F, if it is a false proposition

Answer 4

truth value

Question 5

Propositions that cannot be expressed in terms of simpler
propositions are called

Answer 5

atomic propositions.

Question 6

The area of logic that deals with propositions is called the

Answer 6

propositional calculus or propositional logic

Question 7

It was first developed systematically by the Greek philosopher _____________ more than
2300 years ago.

Answer 7

Aristotle

Question 8

These methods were discussed by the English mathematician George Boole in
1854 in his book

Answer 8

The Laws of Thought.

Question 9

New propositions, called ___________________________ , are formed
from existing propositions using __________________________

Answer 9

compound propositions, logical operators.

Question 10

Let p be a proposition. The negation of p, denoted by ¬p (also denoted by p), is the statement

Answer 10

“It is not the case that p.”

Question 11

The proposition ¬p is read “not p.” The truth value of the negation of p, ¬p, is

Answer 11

the opposite
of the truth value of p.

Question 12

The notation for the negation operator is not standardized. Although ¬p and p are the
most common notations used in mathematics to express the negation of p, other notations you
might see are

Answer 12

∼p, −p, p′
, Np, and !p.

Question 13

The negation of a proposition can also be considered the result of the operation of the

Answer 13

negation operator on a proposition

Question 14

logical operators that are used to form
new propositions from two or more existing propositions

Answer 14

connectives.

Question 15

The conjunction of p and q, denoted by p ∧ q, is the proposition
“p and q.” The conjunction p ∧ q is

Answer 15

true when both p and q are true and is false otherwise

Question 16

The disjunction of p and q, denoted by p ∨ q, is the proposition
“p or q.” The disjunction p ∨ q is false when

Answer 16

n both p and q are false and is true otherwise.

Question 17

The use of the connective or in a disjunction corresponds to one of the two ways the word
or is used in English, namely, as an

Answer 17

inclusive or

Question 18

The exclusive or of p and q, denoted by p ⊕ q (or p XORq), is
the proposition that is true when

Answer 18

exactly one of p and q is true and is false otherwise.

Question 19

“Students who have taken calculus or computer science, but not both, can enroll in this
class.”

Answer 19

e exclusive or

Question 20

The exclusive or of p and q, denoted by p ⊕ q, is the proposition
that is true when exactly

Answer 20

one of p and q is true and is false otherwise.

Question 21

The conditional statement p → q is the proposition “if p, then
q.” The conditional statement p → q is false when p is true and q is false, and true otherwise.
In the conditional statement p → q, p is called the

Answer 21

hypothesis (or antecedent or premise)
and q is called the conclusion (or consequence).

Question 22

The statement p → q is called a conditional statement because

Answer 22

p → q asserts that q is true
on the condition that p holds

Question 23

A conditional statement is also called an

Answer 23

implication

Question 24

Most programming languages contain statements such as

Answer 24

if p then S,

Question 25

The proposition q → p
is called the

Answer 25

converse of p → q

Question 26

is the proposition ¬q → ¬p.

Answer 26

contrapositive of p → q

Question 27

The proposition ¬p → ¬q is called the

Answer 27

inverse of p → q

Question 28

When two compound propositions always have the same truth value we call them

Answer 28

equivalent

Question 29

” The biconditional statement p ↔ q is true when

Answer 29

p and q have the same truth
values, and is false otherwise. Biconditional statements are also called bi-implications

Question 30

is a symbol with two possible values, namely,
0 (zero) and 1 (one)

Answer 30

bit

Question 31

A variable is called a

Answer 31

Boolean variable

Question 32

correspond to the logical connectives

Answer 32

computer bit operations

Question 33

is a sequence of zero or more bits.

Answer 33

bit string

Question 34

The __________ of this string is the number of _______
in the string.

Answer 34

length, bits

Question 35

We define the bitwise OR, bitwise AND, and
bitwise XOR of two strings of the same length to be

Answer 35

the strings that have as their bits the OR,
AND, and XOR of the corresponding bits in the two strings, respectively