1: Module Basic Logic Theme 1: Propositions
English sentences are either true or false or neither. Consider the following sentences: 1. Warsaw is the capital of Poland. 2.
.
3. How are you? The first sentence is true, the second is false, while the last one is neither true nor false. A statement that is either true or false but not both is called a proposition. Propositional logic deals with such statements and compound propositions that combine together simple propositions (e.g., combining sentences (1) and (2) above we may say "Warsaw is the capital of Poland and "). In order to build compound propositions we need rules on how to combine propositions. We denote propositions by lowercase letters , or . Let us define:
The conjunction of and , denoted as
, is the proposition
and it is true when both and are true and false otherwise.
The disjunction of and , denoted as
, is the proposition
and it is false when both and are false and true otherwise.
The negation of , denoted either as It is not true that .
or , is the proposition
Example 1: Let "...
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