What is the name of the logical equivalence $p\land\neg p\equiv\bot$?

Question

The conjunction of any statement $p$ by its negation is a contradiction. That is: $$p\land\neg p\equiv\bot$$ Do you know if there is a name for this logical equivalence?

Answer 1

I have seen both of the following logical equivalencies referred to as negation laws:

$$ p \wedge \neg p \equiv \bot $$ $$ p \vee \neg p \equiv \top $$

You can find this on page $29$ of Discrete Mathematics and its Applications, 8th edition, by Kenneth H. Rosen. Below is an excerpt of Table $6$ from page $29$.

Answer 2

This is the law of non-contradiction.

Non-contradiction is usually presented as: $$\lnot(p\land\lnot p).$$ But $\lnot x$ is just an abbreviation for $x\to\bot$, so this is identical in meaning to $$(p\land\lnot p)\to \bot$$ which is almost exactly what you asked about. The other direction, $\bot \to \ldots$, is trivially true, because $\bot\to x$ for all $x$.

Answer 3

I don't think there is really a consensus on what it is called. The name I most often see is Complement (and that is also how I personally refer to this principle):

However, I have seen Inverse a number of times as well:

And from the Comments and other Answers, apparently there are other names as well.