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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 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.
[b] This is done by polynomial-time reduction from 3-SAT to the other problem. An example of a problem where this method has been used is the clique problem: given a CNF formula consisting of c clauses, the corresponding graph consists of a vertex for each literal, and an edge between each two non-contradicting [c] literals from different ...
The file extension where Microsoft Excel custom toolbar settings are stored. Chart .xlc: A chart created with data from a Microsoft Excel spreadsheet that only saves the chart. To save the chart and spreadsheet save as .XLS. XLC is not supported in Excel 2007 or in any newer versions of Excel. Dialog .xld: Used in older versions of Excel ...
A truth table has one column for each input variable (for example, A and B), and one final column showing all of the possible results of the logical operation that the table represents (for example, A XOR B). Each row of the truth table contains one possible configuration of the input variables (for instance, A=true, B=false), and the result of ...
A matrix B is said to be a square root of A if the matrix product BB is equal to A. [1] Some authors use the name square root or the notation A 1/2 only for the specific case when A is positive semidefinite, to denote the unique matrix B that is positive semidefinite and such that BB = B T B = A (for real-valued matrices, where B T is the ...
Thus Ax = 0 if and only if x is orthogonal (perpendicular) to each of the row vectors of A. It follows that the null space of A is the orthogonal complement to the row space. For example, if the row space is a plane through the origin in three dimensions, then the null space will be the perpendicular line through the origin.
Thus the product AB is defined if and only if the number of columns in A equals the number of rows in B, [1] in this case n. In most scenarios, the entries are numbers, but they may be any kind of mathematical objects for which an addition and a multiplication are defined, that are associative , and such that the addition is commutative , and ...