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biconditional SUBST

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biconditional (logical operator) COMPUT, MAT

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material biconditional (logical operator) COMPUT, MAT

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In that case, in the conditional, the result is true, yet in the biconditional the result is false. en.wikipedia.org

However, it is cloudy if it is raining is not meant as a biconditional, since it can be cloudy while not raining. en.wikipedia.org

Alternative names for biconditional are iff, xnor and bi-implication. en.wikipedia.org

The rule makes it possible to introduce a biconditional statement into a logical proof. en.wikipedia.org

In other words, the contrapositive is logically equivalent to a given conditional statement, though not sufficient for a biconditional. en.wikipedia.org

Except for negation and biconditional, its truth tables are all different from the above. en.wikipedia.org

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements. en.wikipedia.org

Biconditional introduction is the converse of biconditional elimination. en.wikipedia.org

The corresponding logical operations are known, respectively, as conjunction, disjunction, material conditional, biconditional, and negation. en.wikipedia.org

There is clearly no logical equivalence between the two halves of this particular biconditional. en.wikipedia.org

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