SS2 Second Term Further Mathematics Lesson Note – Logical Reasoning

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WEEK NINE

LOGICAL REASONING

CONTENT

(a) Intelligent System

(b) Introduction to Propositional and Predicate Logical Resolution

(c) Introduction to Theorem Proving.

SUB TOPIC: INTELLIGENT SYSTEM

An intelligent system is any formal or informal system designed to:

1. Manage data gathering
2. Obtain and process data
3. Interpret the data with a view to giving reasoned makers for the purpose of taking decision or appropriate action. Intelligent system is also called artificial intelligence.

CLASS ACTIVITY:

1. Define intelligent system
2. List three things intelligent system is designed for

SUB TOPIC: INTRODUCTION TO PROPOSITIONAL AND PREDICATE LOGICAL RESOLUTION

FUNDAMENTAL DEFINITIONS

1. Proposition: this is a written or verbal declarative sentence which is either true or false.
2. True value: the true value of a proposition is the truth or falsity of that proposition. Truth value is denoted as T while false value is denoted as F.
3. Composition proposition: This is a statement that is formed from the combination of two or more simple statement. It is also called compound or molecular proposition.
4. Propositional connectives: These are words or symbols that are used to join two or more simple statements to form composite proposition. The table below shows some propositional connectives.

Connective words                   connective symbols

Not

Or                                            ˅

And                                         ˄

If ……then                                ⇐ or ⇒

If and only if                            ⇔

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