Proposition 2.3.9
Let and be two propositions. Then the two following properties
hold:
(i)
is logically equivalent to
.
(ii)
is logically equivalent to
.
Proof.
We use truth tables.
(i)
T
T
T
F
F
F
F
T
F
T
F
F
T
F
F
T
T
F
T
F
F
F
F
F
T
T
T
T
(ii)
T
T
T
F
F
F
F
T
F
F
T
F
T
T
F
T
F
T
T
F
T
F
F
F
T
T
T
T
In each truth table, the fourth column is identical to the last one,
therefore the claim is true.
Example 2.3.10
The negation of the sentence ``This morning, Dany ate an apple
and an ornage'' is ``This morning, either Dany did not eat an apple or
he did not eat an orange''.
The negation of the sentence ``Theses seats are made either with
leather or with velvet'' is ``These seats are made neither with
leather nor with velvet.''