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A propositional logic formula, also called Boolean expression, is built from variables, operators AND (conjunction, also denoted by ∧), OR (disjunction, ∨), NOT (negation, ¬), and parentheses. A formula is said to be satisfiable if it can be made TRUE by assigning appropriate logical values (i.e. TRUE, FALSE) to
Given a formula X, the negation ¬X is a formula. Given two formulas X and Y, and a binary connective b (such as the logical conjunction ∧), the expression (X b Y) is a formula. (Note the parentheses.) Through this construction, all of the formulas of propositional logic can be built up from propositional variables as a basic unit.
Spaces within a formula must be directly managed (for example by including explicit hair or thin spaces). Variable names must be italicized explicitly, and superscripts and subscripts must use an explicit tag or template. Except for short formulas, the source of a formula typically has more markup overhead and can be difficult to read.
Starting after the second symbol, match the shortest subexpression y of x that has balanced parentheses. If x is a formula, there is exactly one symbol left after this expression, this symbol is a closing parenthesis, and y itself is a formula. This idea can be used to generate a recursive descent parser for formulas. Example of parenthesis ...
Formulas in the B column multiply values from the A column using relative references, and the formula in B4 uses the SUM() function to find the sum of values in the B1:B3 range. A formula identifies the calculation needed to place the result in the cell it is contained within. A cell containing a formula, therefore, has two display components ...
and ) are parentheses / p ə ˈ r ɛ n θ ɪ s iː z / (singular parenthesis / p ə ˈ r ɛ n θ ɪ s ɪ s /) in American English, and either round brackets or simply brackets in British English. [1] [4] They are also known as "parens" / p ə ˈ r ɛ n z /, "circle brackets", or "smooth brackets". In formal writing, "parentheses" is also used ...
An important set of problems in computational complexity involves finding assignments to the variables of a Boolean formula expressed in conjunctive normal form, such that the formula is true. The k -SAT problem is the problem of finding a satisfying assignment to a Boolean formula expressed in CNF in which each disjunction contains at most k ...
With some standard function when there is little chance of ambiguity, it is common to omit the parentheses around the argument altogether (e.g., ). Note that this is never done with a general function f {\displaystyle f} , in which case the parenthesis are always included