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## SS1: MATHEMATICS - 2ND TERM

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Lesson 7, Topic 4
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# Implication

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#### Topic Content:

• Implication
• Simple Statement
• Compound Statement

Introduction:

To understand the concept of logical implication, we need to bring to bear our understanding of logical statements.

Recall, a statement could either be true or false. If statements X and Y are true, then the combination of X and Y is called implication.

### Simple Statement:

This contains a single preposition or idea.

### Compound Statement:

A compound statement contains two or more sub-statements. In practice, statements are usually more complex e.g. “Some graduates in Nigeria are employed and some are unemployed” This is an example of a compound statement. Since it contains a number of simple sub-statements:

Ɛ: Graduates who are in Nigeria

X: Graduates in Nigeria who are employed

~X: Graduates in Nigeria who are unemployed

The Venn diagram below illustrates the given statements.

Recall that ~X and X′ both mean the complement of set X. Note also that Venn diagrams are very useful for showing compound statements. Consider the Venn diagram below:

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