To determine the intersection of events [tex]\( J \)[/tex] and [tex]\( T \)[/tex], we need to find the common elements present in both sets [tex]\( J \)[/tex] and [tex]\( T \)[/tex].
Let's start by listing the elements of each set:
- Set [tex]\( J \)[/tex] includes: [tex]\( \{1, 2, 3, 4, 5, 6\} \)[/tex]
- Set [tex]\( T \)[/tex] includes: [tex]\( \{2, 4, 6, 8, 10\} \)[/tex]
The intersection of two sets is a new set that contains all the elements that are common to both sets. To find this:
1. We look at each element in set [tex]\( J \)[/tex] to see if it is also in set [tex]\( T \)[/tex].
2. If an element from set [tex]\( J \)[/tex] is found in set [tex]\( T \)[/tex], it is included in the intersection set.
Let's go through the elements of set [tex]\( J \)[/tex]:
- [tex]\( 1 \)[/tex] is in set [tex]\( J \)[/tex] but not in set [tex]\( T \)[/tex]. So, it is not part of the intersection.
- [tex]\( 2 \)[/tex] is in both sets [tex]\( J \)[/tex] and [tex]\( T \)[/tex]. So, it is part of the intersection.
- [tex]\( 3 \)[/tex] is in set [tex]\( J \)[/tex] but not in set [tex]\( T \)[/tex]. So, it is not part of the intersection.
- [tex]\( 4 \)[/tex] is in both sets [tex]\( J \)[/tex] and [tex]\( T \)[/tex]. So, it is part of the intersection.
- [tex]\( 5 \)[/tex] is in set [tex]\( J \)[/tex] but not in set [tex]\( T \)[/tex]. So, it is not part of the intersection.
- [tex]\( 6 \)[/tex] is in both sets [tex]\( J \)[/tex] and [tex]\( T \)[/tex]. So, it is part of the intersection.
Now, let's summarize the common elements:
- The common elements are [tex]\( 2, 4, \)[/tex] and [tex]\( 6 \)[/tex].
Therefore, the set that represents the intersection of events [tex]\( J \)[/tex] and [tex]\( T \)[/tex] is:
[tex]\[ J \cap T = \{2, 4, 6\} \][/tex]
