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Venn diagram of (true part in red) In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence 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.
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 ...
Because of dependencies between the items (for example, if solving item j implies solving item i) not all elements of the power set of Q will, in general, be possible knowledge states. The set of all possible knowledge states is called the knowledge structure. Methods of Boolean analysis can be used to construct a knowledge structure from data ...
expression 1, expression 2: Expressions with values of any type. If the condition is evaluated to true, the expression 1 will be evaluated. If the condition is evaluated to false, the expression 2 will be evaluated. It should be read as: "If condition is true, assign the value of expression 1 to result.
The material conditional is also notated using the infixes and . [2] In the prefixed Polish notation , conditionals are notated as C p q {\displaystyle Cpq} . In a conditional formula p → q {\displaystyle p\to q} , the subformula p {\displaystyle p} is referred to as the antecedent and q {\displaystyle q} is termed the consequent of the ...
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The condition is evaluated true or false as a Boolean expression. On the basis of the evaluation of the Boolean condition, the entire expression returns value_if_true if condition is true, but value_if_false otherwise. Usually the two sub-expressions value_if_true and value_if_false must have the same type, which determines the type of the whole