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In writing, phrases commonly used as alternatives to P "if and only if" Q include: Q is necessary and sufficient for P, for P it is necessary and sufficient that Q, P is equivalent (or materially equivalent) to Q (compare with material implication), P precisely if Q, P precisely (or exactly) when Q, P exactly in case Q, and P just in case Q. [3]
One type of situation is referred to above under zero conditional, where will expresses futurity, but the sentence as a whole expresses factual implication rather than a potential future circumstance: "If aspirins will cure it, I'll take a couple tonight" (the taking is not a consequence of the curing, but a consequence of the expectation that ...
A conditional sentence is a sentence in a natural language that expresses that one thing is contingent on another, e.g., "If it rains, the picnic will be cancelled." They are so called because the impact of the sentence’s main clause is conditional on a subordinate clause.
The detailed semantics of "the" ternary operator as well as its syntax differs significantly from language to language. A top level distinction from one language to another is whether the expressions permit side effects (as in most procedural languages) and whether the language provides short-circuit evaluation semantics, whereby only the selected expression is evaluated (most standard ...
One may summarize any, and thus all, of these cases by the statement "P if and only if Q", which is denoted by , whereas cases tell us that is identical to . For example, in graph theory a graph G is called bipartite if it is possible to assign to each of its vertices the color black or white in such a way that every edge of G has one endpoint ...
In practice it has been observed that most arithmetic IF statements reference the following statement with one or two of the labels. This was the only conditional control statement in the original implementation of Fortran on the IBM 704 computer. On that computer the test-and-branch op-code had three addresses for those three states.
A sentence consisting of at least one dependent clause and at least two independent clauses may be called a complex-compound sentence or compound-complex sentence. Sentence 1 is an example of a simple sentence. Sentence 2 is compound because "so" is considered a coordinating conjunction in English, and sentence 3 is complex. Sentence 4 is ...
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.