May 2024
Intermediate to advanced
332 pages
15h 45m
English
Content preview from Discrete Mathematics
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---------------------------
SYMBOUC
LOGIC
61
1.8
WHY USE
LOGICAL
EQUIVALENCES
The main reason we study logical equivalences is because two expressions can often look very different and
yet be the same.
By
using truth tables, we can see that this is so. Furthermore, we often use equivalences to
simplify expressions, so that it is easier to read.
1.9
TAUTOLOGIES AND CONTRADICTIONS
Definition A tautology is a Boolean expression which always results
in
a true result, regardless
of
what the
Boolean variables in the expression are assigned to.
We saw this earlier on, with the expression (p v -,p
).
If
v(p) =
T,
then the whole expression is true. ...
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