To determine whether the sets [tex]\(\{2, 4, 6\}\)[/tex] and [tex]\(\{6, 4, 2\}\)[/tex] are equal or not, let's recall the properties of sets in mathematics:
1. Definition of a Set: A set is a collection of distinct objects, considered as an object in its own right.
2. Order of Elements: In a set, the order of elements does not matter. Hence, [tex]\(\{2, 4, 6\}\)[/tex] is considered the same as [tex]\(\{6, 4, 2\}\)[/tex].
3. Equality of Sets: Two sets are considered equal if they contain exactly the same elements, regardless of the order of those elements.
Given the sets:
[tex]\[
\{2, 4, 6\} \quad \text{and} \quad \{6, 4, 2\}
\][/tex]
Let's compare their elements:
- Both sets contain the element [tex]\(2\)[/tex].
- Both sets contain the element [tex]\(4\)[/tex].
- Both sets contain the element [tex]\(6\)[/tex].
Since both sets contain exactly the same elements, they are equal by the definition of set equality.
Thus, the correct symbol to use is [tex]\( = \)[/tex]. So, the expression
[tex]\[
\{2, 4, 6\} = \{6, 4, 2\}
\][/tex]
is true.
