Final answer:
The statement that every language defined by a Finite Automaton (FA) can also be defined by a Transition Graph (TG) is true, as FAs are a form of TGs and both models describe regular languages in formal language theory.
Step-by-step explanation:
The question you've asked refers to whether any language defined by a Finite Automaton (FA) can also be defined by a Transition Graph (TG). The answer is True. Finite automata and transition graphs are both abstract computational models used in computer science to describe languages, with finite automata being a simple form of transition graphs. In formal language theory, finite automata are often used to represent regular languages, which are the simplest class of languages recognized by these models.
To understand why this is true, consider that a finite automaton consists of states and transitions between these states based on input symbols. Similarly, a transition graph also consists of states and transitions, but it is a graphical representation. As such, every FA can be represented as a TG, where the states and transitions map directly to nodes and edges in the graph. This implies that the set of strings accepted by the FA corresponds to the paths recognized by the TG, and hence, they define the same language.
In terms of logic, if we know that all gazintz are gazatz, and all gazatz are garingers, then we can logically conclude that all gazintz are garingers, based on transitive property. Similarly, if FA and TG can both define a certain class of languages (regular languages), we can conclude that every language defined by FA can also be defined by TG.