Formal Methods in Software Engineering Lecture # 05 rules of inference and logical deductions Instructor: Saima Zareen Assistant Professor Department of Software Engineering saima.zareen@uettaxila.edu.pk

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

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

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.

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

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

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?

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

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Questions