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In current practice, the single 'word' "iff" is almost always read as the four words "if and only if". However, in the preface of General Topology , Kelley suggests that it should be read differently: "In some cases where mathematical content requires 'if and only if' and euphony demands something less I use Halmos' 'iff ' ".
Example 2 For the whole numbers greater than two, being odd is necessary to being prime, since two is the only whole number that is both even and prime. Example 3 Consider thunder, the sound caused by lightning. One says that thunder is necessary for lightning, since lightning never occurs without thunder. Whenever there is lightning, there is ...
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.
The conjunction sī is only rarely used in classical Latin to introduce indirect questions, although this usage is found in medieval Latin and is common in Greek and in modern Romance languages such as French and Italian. The use of 'if' to make a wish, found in ancient Greek, is not usual in Latin, except sometimes in poetry.
Many techniques are employed by logicians to represent an argument's logical form. A simple example, applied to two of the above illustrations, is the following: Let the letters 'P', 'Q', and 'S' stand, respectively, for the set of men, the set of mortals, and Socrates. Using these symbols, the first argument may be abbreviated as: All P are Q.
By the completeness theorem of first-order logic, a statement is universally valid if and only if it can be deduced using logical rules and axioms, so the Entscheidungsproblem can also be viewed as asking for an algorithm to decide whether a given statement is provable using the rules of logic.
For example: Early Retirement : those who subscribe to the F.I.R.E. (Financial Independence Retire Early) philosophy look to aggressively save and invest to build up large nest eggs as quickly as ...
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.