TMA1201 Discrete Structures & Probability
Faculty of Computing & Informatics
Multimedia University
,What you will learn in this lecture:
• Arguments
• Premises
• Conclusions
• 8 Rules of Inference
– Addition
– Simplification
– Modus Ponens
– Modus Tollens
– Hypothetical Syllogism
– Disjunctive Syllogism
– Resolution
– Conjunction
• 4 Additional Rules of Inference for Predicates
2
TMA1201 Discrete Structures & Probability, Faculty of Computing & Informatics, MMU
,Reasoning:
a cognitive process of looking for reasons, beliefs, and conclusions.
In mathematics, you have Sequences of Compound
Propositions / Predicates
as Arguments
Rules of
and you use Inference as
Proper
Reasoning Rules
to finally get a Valid Conclusion
3
TMA1201 Discrete Structures & Probability, Faculty of Computing & Informatics, MMU
, Formal Reasoning is proving.
Proof is a part of problem solving.
Basically, if you think that you have found some hypotheses, and you think
that these hypotheses are true, then you may wish to show and figure out
why and how they are true.
However, it is not necessary that these hypotheses will be true in all cases,
sometimes they can be false.
4
TMA1201 Discrete Structures & Probability, Faculty of Computing & Informatics, MMU
Faculty of Computing & Informatics
Multimedia University
,What you will learn in this lecture:
• Arguments
• Premises
• Conclusions
• 8 Rules of Inference
– Addition
– Simplification
– Modus Ponens
– Modus Tollens
– Hypothetical Syllogism
– Disjunctive Syllogism
– Resolution
– Conjunction
• 4 Additional Rules of Inference for Predicates
2
TMA1201 Discrete Structures & Probability, Faculty of Computing & Informatics, MMU
,Reasoning:
a cognitive process of looking for reasons, beliefs, and conclusions.
In mathematics, you have Sequences of Compound
Propositions / Predicates
as Arguments
Rules of
and you use Inference as
Proper
Reasoning Rules
to finally get a Valid Conclusion
3
TMA1201 Discrete Structures & Probability, Faculty of Computing & Informatics, MMU
, Formal Reasoning is proving.
Proof is a part of problem solving.
Basically, if you think that you have found some hypotheses, and you think
that these hypotheses are true, then you may wish to show and figure out
why and how they are true.
However, it is not necessary that these hypotheses will be true in all cases,
sometimes they can be false.
4
TMA1201 Discrete Structures & Probability, Faculty of Computing & Informatics, MMU
