Search results
Results from the WOW.Com Content Network
In logic and mathematics, inclusion is the concept that all the contents of one object are also contained within a second object. [ 1 ] For example, if m and n are two logical matrices , then
The following proposition says that for any set , the power set of , ordered by inclusion, is a bounded lattice, and hence together with the distributive and complement laws above, show that it is a Boolean algebra.
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.
Inclusion–exclusion illustrated by a Venn diagram for three sets. Generalizing the results of these examples gives the principle of inclusion–exclusion. To find the cardinality of the union of n sets: Include the cardinalities of the sets. Exclude the cardinalities of the pairwise intersections.
For example, if the domain is the set of all real numbers, one can assert in first-order logic the existence of an additive inverse of each real number by writing ∀x ∃y (x + y = 0) but one needs second-order logic to assert the least-upper-bound property for sets of real numbers, which states that every bounded, nonempty set of real numbers ...
Disjunction in natural languages does not precisely match the interpretation of in classical logic. Notably, classical disjunction is inclusive while natural language disjunction is often understood exclusively, as the following English example typically would be. [1] Mary is eating an apple or a pear.
It is sometimes called the inclusive OR gate to distinguish it from XOR, the exclusive OR gate. [4] The behavior of OR is the same as XOR except in the case of a 1 for both inputs. In situations where this never arises (for example, in a full-adder ) the two types of gates are interchangeable.
Pages in category "Logic design" The following 8 pages are in this category, out of 8 total. This list may not reflect recent changes. ...