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Proof by contradiction is similar to refutation by contradiction, [4] [5] also known as proof of negation, which states that ¬P is proved as follows: The proposition to be proved is ¬P. Assume P. Derive falsehood. Conclude ¬P. In contrast, proof by contradiction proceeds as follows: The proposition to be proved is P. Assume ¬P. Derive ...
false (contradiction) bottom, falsity, contradiction, falsum, empty clause propositional logic, Boolean algebra, first-order logic: denotes a proposition that is always false. The symbol ⊥ may also refer to perpendicular lines.
Proofs employ logic expressed in mathematical symbols, ... In addition to theorems of geometry, ... this takes the form of a proof by contradiction in which the ...
A proof by contrapositive is a direct proof of the contrapositive of a statement. [14] However, indirect methods such as proof by contradiction can also be used with contraposition, as, for example, in the proof of the irrationality of the square root of 2 .
Tautology is sometimes symbolized by "Vpq", and contradiction by "Opq". The tee symbol is sometimes used to denote an arbitrary tautology, with the dual symbol representing an arbitrary contradiction; in any symbolism, a tautology may be substituted for the truth value "true", as symbolized, for instance, by "1".
The glyph of the up tack appears as an upside-down tee symbol, and as such is sometimes called eet (the word "tee" in reverse). [citation needed] Tee plays a complementary or dual role in many of these theories. The similar-looking perpendicular symbol ( , \perp in LaTeX, U+27C2 in Unicode) is a binary relation symbol used to represent:
In mathematics, the symbol used to represent a contradiction within a proof varies. [7] Some symbols that may be used to represent a contradiction include ↯, Opq, , ⊥, / , and ※; in any symbolism, a contradiction may be substituted for the truth value "false", as symbolized, for instance, by "0" (as is common in Boolean algebra).
In propositional logic, modus tollens (/ ˈ m oʊ d ə s ˈ t ɒ l ɛ n z /) (MT), also known as modus tollendo tollens (Latin for "mode that by denying denies") [2] and denying the consequent, [3] is a deductive argument form and a rule of inference.