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The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...
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.
In this example, s1 gets executed if and only if a is true and b is true. But what about s2? One person might be sure that s2 gets executed whenever a is false (by attaching the else to the first if), while another person might be sure that s2 gets executed only when a is true and b is false (by attaching the else to the second if). In other ...
Equivalence (if and only if): , , , , (prefix) in which is the most modern and widely used, and is commonly used where is also used. For example, the meaning of the statements it is raining (denoted by p {\displaystyle p} ) and I am indoors (denoted by q {\displaystyle q} ) is transformed, when the two are combined with logical connectives:
Chondromalacia patellae (also known as CMP) is an inflammation of the underside of the patella and softening of the cartilage. The cartilage under the kneecap is a natural shock absorber, and overuse, injury, and many other factors can cause increased deterioration and breakdown of the cartilage.
Hasse diagram of a complemented lattice. A point p and a line l of the Fano plane are complements if and only if p does not lie on l.. In the mathematical discipline of order theory, a complemented lattice is a bounded lattice (with least element 0 and greatest element 1), in which every element a has a complement, i.e. an element b satisfying a ∨ b = 1 and a ∧ b = 0.
There are two main variations of monadic second-order graph logic: MSO 1 in which only vertex and vertex set variables are allowed, and MSO 2 in which all four types of variables are allowed. The predicates on these variables include equality testing, membership testing, and either vertex-edge incidence (if both vertex and edge variables are ...
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 ...