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In logic and mathematics, statements and are said to be logically equivalent if they have the same truth value in every model. [1] The logical equivalence of and is sometimes expressed as , ::, , or , depending on the notation being used.
Logical equality is a logical operator that compares two truth values, or more generally, two formulas, such that it gives the value True if both arguments have the same truth value, and False if they are different.
The assertion that Q is necessary for P is colloquially equivalent to "P cannot be true unless Q is true" or "if Q is false, then P is false". [9] [1] By contraposition, this is the same thing as "whenever P is true, so is Q". The logical relation between P and Q is expressed as "if P, then Q" and denoted "P ⇒ Q" (P implies Q).
In botanical nomenclature, the triple bar denotes homotypic synonyms (those based on the same type specimen), to distinguish them from heterotypic synonyms (those based on different type specimens), which are marked with an equals sign. [15] In chemistry, the triple bar can be used to represent a triple bond between atoms.
The relationship x precedes y is written x ≺ y. The relation x precedes or is equal to y is written x ≼ y. The relationship x succeeds (or follows) y is written x ≻ y. The relation x succeeds or is equal to y is written x ≽ y. [citation needed]
To avoid confusion with the usual equality and membership, these are denoted by ‖ x = y ‖ and ‖ x ∈ y ‖ for x and y in V B. They are defined as follows: ‖ x ∈ y ‖ is defined to be Σ t ∈ Dom(y) ‖ x = t ‖ ∧ y(t) ("x is in y if it is equal to something in y"). ‖ x = y ‖ is defined to be ‖ x ⊆ y ‖∧‖ y ⊆ x ...
ln – natural logarithm, log e. lnp1 – natural logarithm plus 1 function. ln1p – natural logarithm plus 1 function. log – logarithm. (If without a subscript, this may mean either log 10 or log e.) logh – natural logarithm, log e. [6] LST – language of set theory. lub – least upper bound. [1] (Also written sup.)
Random variables are usually written in upper case Roman letters, such as or and so on. Random variables, in this context, usually refer to something in words, such as "the height of a subject" for a continuous variable, or "the number of cars in the school car park" for a discrete variable, or "the colour of the next bicycle" for a categorical variable.