list the subset of each set below
[tex]\LARGE\color{purple}{{{\boxed{\tt{}HERE'S \: THE \: ANSWER!}}}}[/tex]
1. \( \{\mathrm{w}, \mathrm{e}\} \)
Subsets: \( \{\} \) (empty set), \( \{\mathrm{w}\} \), \( \{\mathrm{e}\} \), \( \{\mathrm{w}, \mathrm{e}\} \)
2. \( \{\mathrm{I}\} \)
Subsets: \( \{\} \) (empty set), \( \{\mathrm{I}\} \)
3. \( \{\mathrm{y}, \mathrm{o}, \mathrm{u}\} \)
Subsets: \( \{\} \) (empty set), \( \{\mathrm{y}\} \), \( \{\mathrm{o}\} \), \( \{\mathrm{u}\} \), \( \{\mathrm{y}, \mathrm{o}\} \), \( \{\mathrm{y}, \mathrm{u}\} \), \( \{\mathrm{o}, \mathrm{u}\} \), \( \{\mathrm{y}, \mathrm{o}, \mathrm{u}\} \)
4. \( \{\} \) (empty set)
Subsets: \( \{\} \) (empty set)
[tex]✏ EXPLANATION :[/tex]
Sure! The subsets of a set are all the possible subsets that can be formed by selecting zero, one, or more elements from the original set. Let's go through each set and list their subsets:
1. {w, e}
- Subsets: The possible subsets are:
- {} (empty set): This is a subset that contains no elements.
- {w}: This subset contains the element 'w' from the original set.
- {e}: This subset contains the element 'e' from the original set.
- {w, e}: This subset contains both elements 'w' and 'e' from the original set.
2. {I}
- Subsets: The possible subsets are:
- {} (empty set): This is a subset that contains no elements.
- {I}: This subset contains the element 'I' from the original set.
3. {y, o, u}
- Subsets: The possible subsets are:
- {} (empty set): This is a subset that contains no elements.
- {y}: This subset contains the element 'y' from the original set.
- {o}: This subset contains the element 'o' from the original set.
- {u}: This subset contains the element 'u' from the original set.
- {y, o}: This subset contains both elements 'y' and 'o' from the original set.
- {y, u}: This subset contains both elements 'y' and 'u' from the original set.
- {o, u}: This subset contains both elements 'o' and 'u' from the original set.
- {y, o, u}: This subset contains all three elements 'y', 'o', and 'u' from the original set.
4. {}
- Subsets: The only subset is the empty set itself, which contains no elements.
I hope this explanation clarifies how we determine the subsets of each set.
CarryOnLearning
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