1. Formal Methods in Software Engineering
Lecture # 05
rules of inference and logical deductions
Instructor: Saima Zareen
Assistant Professor
Department of Software Engineering

2. Introduction
This rule states that we can make complex propositions, if we are given simple propositions
Given p we can conclude p or q is true P
_______
P or q
Given q, we can conclude p or q is true Q
________
P or Q

3. Introduction rule of conditional(=>)
If we know q is true, we can conclude p=>q is also true.
[p] Q
-----
P=>q is true

4. Elimination rule
If we are given complex proposition, we can conclude a simple proposition from it.
Given p and q
When p and q is true, it means we can conclude p is true.
P and Q p
When p and q is true, it means we can conclude q is true.

5. Elimination rule of conditional(=>)
Given p is true and p=>q is true, we can conclude q is also true.

6. Elimination rule of negation
Given P and not p= false
If we started with a false statement, we can conclude anything
Given False
We can conclude p
We can conclude q

7. Logic Puzzle
it is rumoured that there is gold buried on the island. You ask one of the natives, A, whether there is gold on the island. He makes the following response:
'There is gold on this island equivales I am a knight.' The
problem is as follows.
(a) Can it be determined whether A is a knight or a knave?
(b) Can it be determined whether there is gold on the island?

8. Let G denote the proposition 'There is gold on the island'
Let G denote the proposition 'There is gold on the island'. A's statement
is A ≡ G. So what we are given is
A≡𝐴≡G

9. Summary

10. Questions