Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Discrete mathematics
Solve the inference problem using the example I provide. Follow the example to solve the question.
Transcribed Image Text:Accepting the following premises:
1.
If it does not rain, or it is not foggy, then the sailing race will be held and the lifesaving demonstration will
go on.
2. If the sailing race is held, then the trophy will be awarded.
3. The trophy was not awarded.
Show that it rained.
Symbolically represent the propositions as follows:
r.
f:
S:
d:
t:
It rained.
It was foggy.
The sailing race was held.
Lifesaving demonstration went on.
Trophy was awarded.
Then we have:
1. (r Vf) → (s Ad)
2. st
3. t
Accepting the premises, it suffices to show r.
And we have r as desired.
4.
nt
18
(s^ d)
(vf)
fרר r Aרר
&
: r^f
r
Premise 3
Modus tollens, Premise 2
Domination
Modus tollens, Premise 1
De Morgan's
Double negation
Conjunctive simplification
Transcribed Image Text:Inference
Accept the following Premises
1.
2.
If fish can fly, birds can Swim
If birds can swim, squirrels can
talk
If birds can swim and squirrels
can talk, capybaras can write.
3. If
4. Fish can fly
Show, using the rules of inference,
that capybaras can write
Expert Solution
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Step 1
Given:
1. If fish can fly, birds can swim.
2. If birds can swim, squirrels can talk.
3. If birds can swim and squirrels can talk, capybaras can write.
4. Fish can fly.
We have to show using inference, that capybaras can write.
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