Decide if the given statement is true or false. If it is false, give the reason. \( \{3,9,4\} \subset\{3,4,9\} \) Choose the correct answer below. A. This statement is true. B. This statement is false. No set is a proper subset of itself. C. This statement is false. The second set is a proper subset of the first set, not the other way around. D. This statement is false. The elements of the two sets are not in the same order. E. This statement is false. The second set does not contain all the elements present in the first set.

A. This statement is true. The first set \( \{3,9,4\} \) is indeed a subset of \( \{3,4,9\} \) because a subset only requires that all the elements in the first set are contained within the second set, regardless of order. In set theory, the order of elements does not matter, so both sets have the same elements. Set theory has a rich historical background, originating from the work of mathematicians like Georg Cantor in the late 19th century, when the concept of infinity and set operations transformed how mathematicians viewed and conducted their work. The exploration of ordered versus unordered sets lent itself to deeper understanding, leading to foundational developments in various branches of mathematics. In real-world applications, understanding subsets is crucial in areas such as data science and computer programming. For example, when filtering or sorting data, you often check if a collection of items (a subset) belongs to or is part of a larger data set, which helps to streamline processes, optimize efficiency, and make better data-driven decisions.