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The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...
is true only if both A and B are false, or both A and B are true. Whether a symbol means a material biconditional or a logical equivalence , depends on the author’s style. x + 5 = y + 2 ⇔ x + 3 = y {\displaystyle x+5=y+2\Leftrightarrow x+3=y}
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.
Since the statement and the converse are both true, it is called a biconditional, and can be expressed as "A polygon is a quadrilateral if, and only if, it has four sides." (The phrase if and only if is sometimes abbreviated as iff.) That is, having four sides is both necessary to be a quadrilateral, and alone sufficient to deem it a quadrilateral.
This statement expresses the idea "' if and only if '". In particular, the truth value of p ↔ q {\displaystyle p\leftrightarrow q} can change from one model to another. On the other hand, the claim that two formulas are logically equivalent is a statement in metalanguage , which expresses a relationship between two statements p {\displaystyle ...
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The government has said that it only targets dual citizens who work or settle in the country. But a 2019 case showed that short-term visits could still go wrong. But a 2019 case showed that short ...
An argument is valid if and only if its corresponding conditional is a logical truth. It follows that an argument is valid if and only if the negation of its corresponding conditional is a contradiction. Therefore, the construction of a corresponding conditional provides a useful technique for determining the validity of an argument.