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Negation operator

In this step, we will introduce the negation operator.
So far we have looked at the following operators:

• Conjunction operator
• Disjunction operator
• Exclusive disjunction operator

In this step, we will introduce the negation operator.

The negation operator

In spoken English it is common to negate a proposition. Consider the proposition “I do not like cake”, or “It is not the case that I enjoy dog walking”. Both of the propositions essentially state the opposite of a simpler proposition:

• In the case of the proposition “I do not like cake”, it is stating the opposite (negation) of “I like cake”.
• In the case of the proposition “It is not the case that I enjoy dog walking”, it is stating the opposite (negation) of the proposition “I enjoy dog walking”.

This concept is called negation.

In logic we have a symbol that represents the negation of a proposition. Let (p) represent the proposition “I like dogs”. The negation of the statement is “it is not the case that I like dogs” and is represented as (neg p), which is read as “not p”.

The tabular presentation of the negation is shown below. Notice that in this table there are only two rows (excluding the header). This is because the negation operator is a unary operator which means that it is applied to only one proposition whereas the conjunction and disjunction operators are binary operators which mean they are applied to exactly two propositions.

In the next step, we will look at another operator, the implication operator, and how it differs from the previously introduced operators.