Chapter 2: Logic

Question 1

Statement

Answer 1

A statement is a declarative sentence that is either true or false.

Question 2

Truth value

Answer 2

Every statement has a truth value, namely true (T) or false (F).

Question 3

Negation

Answer 3

The negation of the statement P is ~P, and it has the opposite truth value

Question 4

Disjunction

Answer 4

The disjunction of statements P and Q is the statement P V Q, read “P or Q”. P V Q is false only if both P and Q are false, otherwise it’s true

Question 5

Conjunction

Answer 5

The conjunction of statements P and Q is the statement P ^ Q, read P and Q; P ^ Q is true only if both P and Q are true, otherwise it’s false

Question 6

Implication

Answer 6

For the statements P and Q, the implication statement “if P, then Q” is denoted as P => Q; the statement P is called the hypothesis or the sufficient condition; the statement Q is called the conclusion or the necessary condition

Question 7

Converse

Answer 7

The converse of an implication Q => P

Question 8

Biconditional

Answer 8

The biconditional statement for P and Q is P <=> Q : (P => Q) ^ (Q => P); in words “P if and only if Q”

Question 9

Open sentence

Answer 9

An open sentence is a declarative sentence that contains one or more variables, each from a domain set. The assignment for each variable creates a statement.