Sure, let's solve this step by step using the information provided in the table:
(a) Choose a set that is equivalent, but not equal, to the set of Dan's favorite menu items.
To answer this question, we would need a set of items that contains the same elements as Dan's set [tex]\(\{Samosa, Hummus, Brisket, Ravioli, Dumplings\}\)[/tex], but represented differently in some sense. However, from the table and given information, there are no sets that are equivalent (contain the same elements) but not exactly identical with respect to Dan's favorite set. Therefore, the answer here would be an empty set: [tex]\(\emptyset\)[/tex].
(b) Choose a set that is equal to the set of Ahmad's favorite menu Items.
Ahmad’s favorite menu items are: [tex]\(\{Fries, Ribs, Jambalaya\}\)[/tex]. We need to find another customer who has exactly these favorite items. From the table, Ivan’s favorite items are also [tex]\(\{Fries, Ribs, Jambalaya\}\)[/tex].
Hence, the customers with a set equal to Ahmad's are:
- Ivan
- Ahmad
(c) Find two customers whose sets of favorite menu items are neither equivalent nor equal.
To solve this, identify customer pairs whose favorite items are completely different without any subset relationships. From the table, there are multiple pairs that satisfy this condition. One example pair is:
- Ivan (\{Ribs, Jambalaya, Fries\})
- Shen (\{Samosa, Hamburger, Fries, Gumbo\})
Another example pair is:
- Shen (\{Samosa, Hamburger, Fries, Gumbo\})
- Charlie (\{Chowder, Tacos\})
Therefore, one example answer is:
Shen and Charlie
In summary:
(a) No equivalent but not equal sets for Dan: [tex]\(\emptyset\)[/tex]
(b) Sets equal to Ahmad: Ivan, Ahmad (mark both)
(c) Example pairs of customers whose sets are neither equivalent nor equal:
- Shen and Charlie
- There are multiple possible correct pairs in the table.
