To solve this question, we'll start by defining the sets based on the information provided:
- [tex]\( G \)[/tex] represents the set of students appearing for General Knowledge: \{Acel, Acton, Anael, Max, Carl, Dario\}
- [tex]\( M \)[/tex] represents the set of students appearing for Math: \{Barek, Bay, Max, Kai, Anael, Carlin\}
- [tex]\( S \)[/tex] represents the set of students appearing for Science: \{Carlin, Acton, Anael, Kai, Dario, Barek\}
Step 1: Find the intersection of sets [tex]\( G \)[/tex] and [tex]\( M \)[/tex]
The intersection of two sets includes all elements that are present in both sets. So, we need to find the common elements between [tex]\( G \)[/tex] and [tex]\( M \)[/tex].
- [tex]\( G = \{Acel, Acton, Anael, Max, Carl, Dario\} \)[/tex]
- [tex]\( M = \{Barek, Bay, Max, Kai, Anael, Carlin\} \)[/tex]
Common elements between [tex]\( G \)[/tex] and [tex]\( M \)[/tex]:
- Anael
- Max
Therefore, [tex]\( G \cap M = \{ Anael, Max \} \)[/tex].
Step 2: Find the union of sets [tex]\( G \)[/tex] and [tex]\( S \)[/tex]
The union of two sets includes all elements from both sets, without duplicates. So, we need to combine all the elements from [tex]\( G \)[/tex] and [tex]\( S \)[/tex].
- [tex]\( G = \{Acel, Acton, Anael, Max, Carl, Dario\} \)[/tex]
- [tex]\( S = \{Carlin, Acton, Anael, Kai, Dario, Barek\} \)[/tex]
Combining all elements from [tex]\( G \)[/tex] and [tex]\( S \)[/tex]:
- Acel
- Acton
- Anael
- Max
- Carl
- Dario
- Carlin
- Kai
- Barek
Therefore, [tex]\( G \cup S = \{ Acel, Acton, Anael, Max, Carl, Dario, Carlin, Kai, Barek \} \)[/tex].
In summary:
- [tex]\( G \cap M = \{ Anael, Max \} \)[/tex]
- [tex]\( G \cup S = \{ Acel, Acton, Anael, Max, Carl, Dario, Carlin, Kai, Barek \} \)[/tex]
