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The biconditional is true in two cases, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence), [2] and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of ...
Venn diagram of (true part in red) In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or bidirectional implication or biimplication or bientailment, is the logical connective used to conjoin two statements and to form the statement "if and only if" (often abbreviated as "iff " [1]), where is known as the antecedent, and the consequent.
When the condition refers to the past, but the consequence to the present, the condition clause is in the past perfect (as with the third conditional), while the main clause is in the conditional mood as in the second conditional (i.e. simple conditional or conditional progressive, but not conditional perfect).
A conditional statement may refer to: A conditional formula in logic and mathematics, which can be interpreted as: Material conditional; Strict conditional; Variably strict conditional; Relevance conditional; A conditional sentence in natural language, including: Indicative conditional; Counterfactual conditional; Biscuit conditional
In mathematics, theorems are often stated in the form "P is true if and only if Q is true". Because, as explained in previous section, necessity of one for the other is equivalent to sufficiency of the other for the first one, e.g. P ⇐ Q {\displaystyle P\Leftarrow Q} is equivalent to Q ⇒ P {\displaystyle Q\Rightarrow P} , if P is necessary ...
The indicative conditional uses the present tense forms "owns" and "beats" and therefore conveys that the speaker is agnostic about whether Sally in fact owns a donkey. The counterfactual example uses the fake tense form "owned" in the "if" clause and the past-inflected modal "would" in the "then" clause. [1]
The "if"-clause of a conditional sentence is called the protasis, and the consequent or main clause is called the apodosis. The negative particle in a conditional clause is usually μή (mḗ), making the conjunctions εἰ μή (ei mḗ) or ἐὰν μή (eàn mḗ) "unless", "if not". However, some conditions have οὐ (ou). [1]
The fragment of second-order logic consisting only of existential second-order formulas is called existential second-order logic and abbreviated as ESO, as , or even as ∃SO. The fragment of Π 1 1 {\displaystyle \Pi _{1}^{1}} formulas is defined dually, it is called universal second-order logic.
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