Find the intersection of the sets. {s,e,t}∩{t,e,s}

Verified step by step guidance

1. Identify the two sets given: Set A = \({\{s, e, t\}}\) and Set B = \({\{t, e, s\}}\).
2. Recall that the intersection of two sets, denoted by \({\cap}\), consists of all elements that are common to both sets.
3. List the elements of Set A and check which of these elements also appear in Set B.
4. Since both sets contain the elements \({s}\), \({e}\), and \({t}\), all elements are common to both sets.
5. Therefore, the intersection \({\{s, e, t\} \cap \{t, e, s\}}\) is the set containing all these common elements.

Key Concepts

Set Theory Basics

Set theory studies collections of distinct objects called sets. Understanding what a set is and how elements are grouped is fundamental to solving problems involving sets, such as finding intersections or unions.

Intersection of Sets

The intersection of two sets includes all elements that are common to both sets. It is denoted by the symbol ∩. For example, the intersection of {a, b, c} and {b, c, d} is {b, c}.

Order and Uniqueness in Sets

In sets, the order of elements does not matter, and each element is unique. Thus, {s, e, t} and {t, e, s} represent the same set, which affects how intersections are determined.