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If and only if. In logic and related fields such as mathematics and philosophy, " if and only if " (often shortened as " iff ") is paraphrased by the biconditional, a logical connective [1] between statements. The biconditional is true in two cases, where either both statements are true or both are false. The connective is biconditional (a ...
In computer science, conditionals (that is, conditional statements, conditional expressions and conditional constructs) are programming language constructs that perform different computations or actions or return different values depending on the value of a Boolean expression, called a condition. Conditionals are typically implemented by ...
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.
In logic and mathematics, necessity and sufficiency are terms used to describe a conditional or implicational relationship between two statements. For example, in the conditional statement: "If P then Q ", Q is necessary for P, because the truth of Q is guaranteed by the truth of P. (Equivalently, it is impossible to have P without Q, or the ...
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 ...
In logic, two propositions and are mutually exclusive iff it is not logically possible for them to be true at the same time; that is, () is a tautology. To say that more than two propositions are mutually exclusive, depending on the context, means either 1. "() () is a tautology" (it is not logically possible for more than one proposition to be true) or 2. "() is a tautology" (it is not ...
In logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions " p is the case " and " p is not the case " are mutually exclusive.
And like Trump, she’s promised to end taxes on tips. She’s also pledged not to raise taxes on households making less than $400,000 annually. Both would growon the deficit. Taken together, the ...