Introduction
Laws of Logic
Discrete Mathematics
Andrei Bulatov
Discrete Mathematics – Laws of Logic
42
Previous Lecture
Truth tables
Tautologies and contradictions
Logic equivalences
Discrete Mathematics – Laws of Logic
43
Logic Equivalences
Compound statements
Φ
and
Ψ
are said to be
logically
equivalent
if the statement
Φ
is true (false) if and only if
Ψ
is
true (respectively, false)
or
The truth tables of
Φ
and
Ψ
are equal
or
For any choice of truth values of the primitive statements
(propositional variables) of
Φ
and
Ψ
,
formulas
Φ
and
Ψ
have
the same truth value
If
Φ
and
Ψ
are logically equivalent, we write
Φ ⇔ Ψ
Discrete Mathematics – Laws of Logic
44
Why Logic Equivalences
To simplify compound statements
``If you are a computer science major or a freshman and you are
not a computer science major or you are granted access to the
Internet, then you are a freshman or have access to the Internet’’
To convert complicated compound statements to certain `normal
form’ that is easier to handle
Conjunctive Normal Form
CNF
Discrete Mathematics – Laws of Logic
45
Example Equivalences
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 Spring '08
 PEARCE
 Computer Science, Logic

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