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The modern symbol for inclusion first appears in Gergonne (1816), who defines it as one idea 'containing' or being 'contained' by another, using the backward letter 'C' to express this. Peirce articulated this clearly in 1870, arguing also that inclusion was a wider concept than equality, and hence a logically simpler one. [ 2 ]
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.
The situation that appears in the derangement example above occurs often enough to merit special attention. [7] Namely, when the size of the intersection sets appearing in the formulas for the principle of inclusion–exclusion depend only on the number of sets in the intersections and not on which sets appear. More formally, if the intersection
A derived binary relation between two sets is the subset relation, also called set inclusion. If all the members of set A are also members of set B, then A is a subset of B, denoted A ⊆ B. For example, {1, 2} is a subset of {1, 2, 3}, and so is {2} but {1, 4} is not. As implied by this definition, a set is a subset of itself.
Pages in category "Logic design" The following 8 pages are in this category, out of 8 total. This list may not reflect recent changes. ...
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.
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A page from Hamilton's Lectures on Logic; the symbols A, E, I, and O refer to four types of categorical statement which can occur in a syllogism (see descriptions, left) The small text to the left erroneously says: "The first employment of circular diagrams in logic improperly ascribed to Euler. To be found in Christian Weise", a book which was ...