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The logic alphabet, also called the X-stem Logic Alphabet (XLA), constitutes an iconic set of symbols that systematically represents the sixteen possible binary truth functions of logic. The logic alphabet was developed by Shea Zellweger. The major emphasis of his iconic "logic alphabet" is to provide a more cognitively ergonomic notation for ...
Generalizing from geometrical symmetry in the previous section, one can say that a mathematical object is symmetric with respect to a given mathematical operation, if, when applied to the object, this operation preserves some property of the object. [15] The set of operations that preserve a given property of the object form a group.
An example is the relation "is equal to", because if a = b is true then b = a is also true. If R T represents the converse of R, then R is symmetric if and only if R = R T. [2] Symmetry, along with reflexivity and transitivity, are the three defining properties of an equivalence relation. [1]
Symmetry occurs not only in geometry, but also in other branches of mathematics. Symmetry is a type of invariance: the property that a mathematical object remains unchanged under a set of operations or transformations. [1] Given a structured object X of any sort, a symmetry is a mapping of the object onto itself which preserves the structure.
A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has, for instance, zero rise time and unlimited fan-out, or it may refer to a non-ideal physical device [1] (see ...
Symmetric and transitive: The relation R on N, defined as aRb ↔ ab ≠ 0. Or any partial equivalence relation; Reflexive and symmetric: The relation R on Z, defined as aRb ↔ "a − b is divisible by at least one of 2 or 3." Or any dependency relation. Properties definable in first-order logic that an equivalence relation may or may not ...
In some fonts (for example Arial) they are only symmetrical in certain sizes. Alternatively the quotes can be rendered as ⌈ and ⌉ (U+2308 and U+2309) or by using a negation symbol and a reversed negation symbol ⌐ ¬ in superscript mode.)
Graph showing the symmetry of the addition function = + Some forms of symmetry can be directly linked to commutativity. When a commutative operation is written as a binary function z = f ( x , y ) , {\displaystyle z=f(x,y),} then this function is called a symmetric function , and its graph in three-dimensional space is symmetric across the ...