<Dd> ∗ 3 ⋅ 24 . ⊢ . ∼ (p . ∼ p) (\ displaystyle \ mathbf (* 3 \ cdot 24). \ \ \ vdash . \ thicksim (p. \ thicksim p)) </Dd> <P> The law of non-contradiction, along with its complement, the law of excluded middle (the third of the three classic laws of thought) and the law of identity (the first of the three classic laws of thought), partitions its logical Universe into exactly two parts; it creates a dichotomy wherein the two parts are "mutually exclusive" and "jointly exhaustive". The law of non-contradiction is merely an expression of the mutually exclusive aspect of that dichotomy, and the law of excluded middle, an expression of its jointly exhaustive aspect . </P> <Table> <Tr> <Td> </Td> <Td> This section needs additional citations for verification . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed . (July 2016) (Learn how and when to remove this template message) </Td> </Tr> </Table> <Tr> <Td> </Td> <Td> This section needs additional citations for verification . Please help improve this article by adding citations to reliable sources . Unsourced material may be challenged and removed . (July 2016) (Learn how and when to remove this template message) </Td> </Tr>

The principle of non-contradiction states that all instances of contradiction are what