Final Answer:
The set of states that share a border with Texas is {Arkansas, Louisiana, Oklahoma, New Mexico}.
Step-by-step explanation:
The set notation {Arkansas, Louisiana, Oklahoma, New Mexico} represents the members of the set of states that share a border with Texas. In this context, the elements inside the curly braces denote the specific states that have a physical boundary with Texas. Texas shares its border to the east with Louisiana, to the northeast with Arkansas, to the north with Oklahoma, and to the west with New Mexico.
The use of set notation is a concise and clear way to list and represent the distinct elements of a set, providing a mathematical and formal expression for the relationship between Texas and its neighboring states.
This set is defined by the geographical proximity of these states to Texas, highlighting the spatial connections between them. Set notation is a fundamental concept in mathematics, allowing us to express relationships and groupings in a standardized and unambiguous manner. In this case, it helps convey the specific set of states that form a border with Texas, facilitating a clear understanding of the regional context.