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Equivalence
Definition 2.3.17
Let
and
be two propositions. The equivalence
is true whenever
and
have the same logical value.
T
T
T
T
F
F
F
T
F
F
F
T
Proposition 2.3.18
For any two propositions
and
,
is logically equivalent to
.
Proof
. We build a truth table:
T
T
T
T
T
T
T
F
F
F
T
F
F
T
F
T
F
F
F
F
T
T
T
T
As the third column and the last column are identical, the claim is true.
root 2002-06-10