April 2024
Intermediate to advanced
832 pages
29h 31m
English
Content preview from Design and Analysis of Algorithms
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616 Design and Analysis of Algorithms
Generally a proof consists of a series of assertions from which the fi nal assertion is derived and that is
the conclusion – the assertion to be proved. For example, a typical inference rule is:
if P → Q and
Q → R then
P → R (conclusion)
There are a number of such Inference Rules which help us in developing a proof. Some of them are:
1. if P then P ∨ Q, can also be written as P ⇒ P ∨ Q
2. if P ∧ Q then P
3. if P, P → Q then Q this rule known as Modus Ponens
4. if ¬Q, P → Q then ¬P Modus Tollens
5. if P ∨ Q, ¬ P then Q
6. if P, Q then P ∧ Q
7. if P → Q, R → S, P ∨ R then Q ∨ S
8. if P → Q, R → S, ¬Q ∨ ¬S then ...
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