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In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
A logical operation meaning "not and"; it produces a true result for all input combinations except the case where all inputs are true. It is a fundamental operation since any logical function can be constructed using only NAND operations. n-ary function
Logical operators over bit vectors (corresponding to finite Boolean algebras) are bitwise operations. But not every usage of a logical connective in computer programming has a Boolean semantic. For example, lazy evaluation is sometimes implemented for P ∧ Q and P ∨ Q , so these connectives are not commutative if either or both of the ...
"Logical" refers to the Boolean logical operations of disjunction, conjunction, and negation between two sequences of bits, in which each bit in one sequence is simply compared to its counterpart in the other sequence. Programmers therefore have the option of working in and applying the rules of either numeric algebra or Boolean algebra as needed.
For example, if given the statements "All humans are mortal" and "Socrates is human" a valid conclusion is "Socrates is mortal". Of course this is a trivial example. In actual logical systems the statements can be numerous and complex. It was realized early on that this kind of analysis could be significantly aided by the use of computers.
Nonetheless, the logic alphabet’s two-dimensional geometric letter shapes along with its group symmetry properties can help ease the learning curve for children and adult students alike, as they become familiar with the interrelations and operations on all 16 binary connectives. Giving children and students this advantage is a decided gain.
Logical conjunction is often used for bitwise operations, where 0 corresponds to false and 1 to true: 0 AND 0 = 0, 0 AND 1 = 0, 1 AND 0 = 0, 1 AND 1 = 1. The operation can also be applied to two binary words viewed as bitstrings of equal length, by taking the bitwise AND of each pair of bits at corresponding positions. For example:
It is used for describing logical operations. Analysis/Calculus – the branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.