Question

list all the subsets of the given set.
{pineapple, pork, grapes}

choose the answer that lists all of the subsets of {pineapple, pork, grapes}.
a. {pineapple}, {pork}, {grapes}, {pineapple, pork},
{pineapple, grapes}, {pork, grapes}

b. {pineapple}, {pork}, {grapes}, {pineapple, pork},
{pineapple, grapes}, {pork, grapes},
{pineapple, pork, grapes}

c. {}, {pineapple}, {pork}, {grapes}, {pineapple, pork}
{pineapple, grapes}, {pork, grapes},
{pineapple, pork, grapes}

d. {}, {pineapple}, {pork}, {grapes}, {pineapple, pork},
{pineapple, grapes}, {pork, grapes}

Explanation:

Step1: Recall subset definition

A subset includes the empty set $\{\}$, all single-element subsets, all two-element subsets, and the original set itself.

Step2: Count total subsets

For a set with $n$ elements, total subsets = $2^n$. Here $n=3$, so $2^3=8$ subsets.

Step3: Match to options

Check which option has 8 subsets: empty set, 3 single-element, 3 two-element, 1 original set.

Answer:

C. {}, {pineapple}, {pork}, {grapes}, {pineapple, pork}, {pineapple, grapes}, {pork, grapes}, {pineapple, pork, grapes}