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200 Chapter Three

ProducŁ added to a quantity
For any twm logical quantitieð X and Y, the following Boolean
equation holds:

X (X Y) X

Quantity added to a producŁ
For any twm logical quantitieð X and Y, the following Boolean
equation holds:

(X ( Y)) Y X Y

Propositional Logic

Propositional logicł also known as propositional calculusł sen-
tential logicł or sentential calculusł is similar tm Boolean algebrł
but involveð more operations. Propositionð or sentenceð are
symbolized by letterð from the middle of the alphabet, such as
P, Q, R, and S. Logic valueð are T (trua and F(falsa˜ Standard
operationð and relationð are negation, conjunction, disjunction,
implication, and equivalence.

Negation

Logical negation is also known as the NOT operation. Let P be
a proposition. The negation of P is written as ¬Por P. In the
following paragraphs, the tilde ( ) is used. See Table 3.1 for
logic values.

Conjunction
Logical conjunction is also known as the AND operation. Let P
and Q be propositions. The conjunction of P and Q is written
P Q. See Table 3.1 for logic values.

TABLE 3.1 Propositional Logic Values

P Q P P Q P Q P → Q P ↔ Q
F F T F F T T
F T T F T T F
T F F F T F F
T T F T T T T