# Dual

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A dual of a logical statement is a sort of inversion of the statement.

## Rigorous definition

Consider a logic statement $Q$. For each individual element or operator in $Q$, we replace:

• $U$ (the universal set) with $\varnothing$ (the empty set) and vice versa.
• $\cup$ with $\cap$ and vice versa.

Such a statement is the dual of the statement. An interesting fact of logic is that if a logical statement is true, then its dual is true.