May 2024
Intermediate to advanced
332 pages
15h 45m
English
Content preview from Discrete Mathematics
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12 DISCRETE MATHEMATIC..._
________________________
_
(c) 61(n+1)
3
-(n+l)
(i)
(n+l)
3
-(n+l)=n
3
-n+3(n
2
+n)
Algebra
(ii) n
2
+n
is even
(iii)
21n
2
+ n Definition
of
I
(iv)
613(n
2
+
n)
Multiplying both sides by 3 (basic properties
of
N)
(v) 61(n
3
-n)+3(n
2
+n)
Divides both terms, so divides sum
(vi) QED
(d) QED
3. QED
Equality
The ideas in this proof are given directly,
in
the order in which they are used. This makes
it
concise and
clear. But this is a different order from the way the ideas arose when we came up with the proof in the first
place. By switching the order around, we have lost information about how we came up with the proof ideas. ...
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