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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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