A formula in first-order logic with no free variable occurrences is called a first-order sentence. These are the formulas that will have well-defined truth values under an interpretation.

Feb 13, 2023 · A first-order reaction is a reaction that proceeds at a rate that depends linearly on only one reactant concentration.

Jul 23, 2025 · First-Order Reactions describe chemical processes where the transformation rate directly depends on the concentration of a single substance. We define first-order reactions as …

To determine if the reaction is first-order, plot the natural logarithm of the concentration versus time and see whether the graph is linear. The reaction will be first-order if the graph is linear …

The set of free variables in a formula is much more important than what all the variables are, since bound variables may be changed without afecting the meaning of the formula: for example,

Since the evaluation of quantified formulas usually requires the evaluation of the formula for all possible elements of the universe, truth tables are unsuited for proving first-order formulas …

| {z } F The scope of ∀x is F. The scope of ∃y is G. The formula reads: “for all x, if p(f (x), x) then there exists a y such that p(f (g(x, y)), g(x, y)) and q(x, f (x))”

Feb 13, 2026 · In formulas of first-order predicate calculus, all variables are object variables serving as arguments of functions and predicates. (In second-order predicate calculus, …

Sample first order formula: ∀x. ∃y. x < y ∧ y ≤ x + 1 “for each x, there exists y such that (x is less than y) and (y is less or equal than x plus one)”

[A] o is the original starting concentration of A. Substituting into the equation, we obtain: ln [A] o = - k (0) + C. Therefore, C = ln [A] o. We now can write the integrated form for first-order …