Final answer:
In First-Order Logic, a variable is typically bound by its closest preceding quantifier, and would not normally be bound by two quantifiers of the same kind.
Step-by-step explanation:
The question of whether a variable in First-Order Logic (FOL) can be bound by two quantifiers of the same kind requires an understanding of the syntax and semantics of FOL. In typical predicate logic, each quantified variable within a formula is bound by its closest preceding quantifier, and it would not be standard form to have the same variable bound by two different quantifiers of the same kind. However, there are forms of expressions in FOL where variables appear within multiple quantifiers, such as nested quantifiers affecting different scopes. Key to understanding the meaning of sentences with quantifiers is the concept of the quantifier's scope, which is the part of the formula where the quantifier has effect.
In the context of mathematical equations, understanding how to manipulate variables and solve for them is essential. For instance, if the equation A × F = B × F is given, where F is not zero, one could divide both sides by F to conclude that A = B. On the other hand, if F could be zero, division would not be permissible, and additional information would be required to conclusively determine if A = B. Identifying the relationships between variables and manipulating equations correctly are vital skills within mathematical reasoning.