NOT

Definition

NOT is a logical operator that reverses a proposition's truth value.

Example:

NOT P

If P is true, then NOT P is false.

If P is false, then NOT P is true.

NOT turns true into false and false into true.

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Simple Example

Let:

P = "It is raining"

Then:

NOT P

means:

It is not raining.

If P is true, NOT P is false.

If P is false, NOT P is true.

NOT denies the proposition it applies to.

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Truth Pattern

NOT has this truth pattern:

P      NOT P
true   false
false  true

NOT only works on one proposition.

Operators like AND and OR combine two propositions.

NOT modifies one proposition.

NOT is a one-input logical operator.

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Double Negation

Applying NOT twice returns the original truth value.

Example:

NOT (NOT P)

If:

P = true

then:

NOT P = false
NOT (NOT P) = true

So:

NOT (NOT P)

has the same truth value as:

P

Double negation cancels out in classical logic.

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NOT In Reasoning

NOT is useful for expressing denial, contradiction, and exclusion.

Example:

P
NOT P

Both cannot be true at the same time in classical logic.

This creates a contradiction.

NOT helps define what conflicts with a statement.

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Final Summary

• NOT reverses a proposition's truth value.
• If P is true, NOT P is false.
• If P is false, NOT P is true.
• NOT applies to one proposition.
• Double negation returns the original truth value.
• NOT is central to contradiction and exclusion.