Que: List all the subsets of the given set. \{steak, pear, mango\} Choose the answer that lists all of the subsets of \{steak, pear, mango\}. A. $$ \{ $$ steak\}, $$ \{ $$ pear $$ \},\{ $$ mango $$ \} $$, ssteak, pear\}, \{steak, mango\}, \{pear, mango\} B. $$ \},\{ $$ steak $$ \},\{ $$ pear $$ \},\{ $$ mango $$ \},\{ $$ steak, pear $$ \} $$, \{steak, mango\}, \{pear, mango\}, \{steak, pear, mango\} C. $$ \{ $$ steak $$ \},\{ $$ pear\}, \{mango\}, \{steak, pear\}, \{steak, mango\}, \{pear, mango\}, \{steak, pear, mango\} D. $$ \},\{ $$ steak $$ \},\{ $$ pear $$ \},\{ $$ mango $$ \},\{ $$ steak, pear\}, \{steak, mango\}, \{pear, mango\}

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To find all the subsets of the set $$\{ \text{steak}, \text{pear}, \text{mango} \}$$, we need to consider all possible combinations of the elements, including the empty set.

The set $$\{ \text{steak}, \text{pear}, \text{mango} \}$$ has 3 elements. The total number of subsets of a set with $$n$$ elements is given by $$2^n$$. In this case, $$n = 3$$, so the total number of subsets is:

$$
2^3 = 8
$$

Now, let's list all the subsets:

1. The empty set: $$\{\}$$
2. Single-element subsets:
   - $$\{\text{steak}\}$$
   - $$\{\text{pear}\}$$
   - $$\{\text{mango}\}$$
3. Two-element subsets:
   - $$\{\text{steak, pear}\}$$
   - $$\{\text{steak, mango}\}$$
   - $$\{\text{pear, mango}\}$$
4. The full set:
   - $$\{\text{steak, pear, mango}\}$$

Now, combining all these, the complete list of subsets is:

$$
\{\}, \{\text{steak}\}, \{\text{pear}\}, \{\text{mango}\}, \{\text{steak, pear}\}, \{\text{steak, mango}\}, \{\text{pear, mango}\}, \{\text{steak, pear, mango}\}
$$

Now, let's analyze the provided options:

- **Option A**: Missing the empty set and the full set.
- **Option B**: Contains a syntax error and is missing the empty set.
- **Option C**: Contains all subsets including the empty set and the full set.
- **Option D**: Contains a syntax error and is missing the empty set.

The correct answer that lists all of the subsets of $$\{ \text{steak}, \text{pear}, \text{mango} \}$$ is:

**C.** $$ \{\}, \{\text{steak}\}, \{\text{pear}\}, \{\text{mango}\}, \{\text{steak, pear}\}, \{\text{steak, mango}\}, \{\text{pear, mango}\}, \{\text{steak, pear, mango}\} $$
The correct answer is option C, which lists all subsets of $$\{ \text{steak}, \text{pear}, \text{mango} \}$$ including the empty set and the full set.

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