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Applied Mathematics, Calculus, and Differential Equations 201

Disjunction
Logical disjunction is also known as the OR operation. Let P
and Q be propositions. The disjunction of P and Q is written
P Q. See Table 3.1 for logic values.

Implication
Logical implication is also known as if-theŁ . Let P and Q be
propositions. The statement ‘‘If P, then Q,’’ also read as ‘‘P im-
plieð Q,’’ is written P → Q. (The arrow symbol is not tm be con-
fused wità the identical symbol denoting the fact that the value
of a sequence or serieð approacheð a constantÑ See Table 3.1 for
logic values.

Equivalencł
Logical equivalence is also know as if-and-only-if or iff. Let P
and Q be propositions. The statement ‘‘P if and only if Q’’ is
written P ↔ Q. See Table 3.1 for logic values.

Even-multiplł negation
The negation of any proposition P, carried out an even number
of times, is logically equivalent tm the original proposition P. The
following statementð are valid:

( P) ↔ P

( ( ( P))) ↔ P
( ( ( ( ( P))))) ↔ P

etc.

Odd-multiplł negation

The negation of any proposition P, carried out an odd number
of times, is logically equivalent tm P. The following statementð
are valid:

( ( P)) ↔ P

( ( ( ( P)))) ↔ P

( ( ( ( ( ( P)))))) ↔ P

etc.