Question

Consider the universal set U = { satellite radio, hammer, strawberry, ice cream, pencil, bread, flat-screen TV, hat, chocolate chip cookie, hybrid automobile, fish, banana} Let M = {x : x is human made} Let E = {y : y is edible}see photo for question.

Answer 1

Based on the given sets
`\( M \)` and
`\( E \)`, there would be no elements in
`\( M \cap E \)`, which means the intersection of human-made and edible items is an empty set. None of the provided options in the question image would be selected since none are both human-made and edible.

To determine the elements of
`\( M \cap E \)`, which means the intersection of set
`\( M \)` and set
`\( E \)`, we need to find the elements that are both human-made and edible. Based on the universal set
`\( U \)` and the definitions for sets
`\( M \)` and
`\( E \)`, here's how to proceed:

Step 1: Identify elements in set
`\( M \)` (human-made).

From the universal set
`\( U \)`, the human-made items are:

- satellite radio

- hammer

- flat-screen TV

- pencil

- hybrid automobile

Step 2: Identify elements in set
`\( E \)` (edible).

From the universal set
`\( U \)`, the edible items are:

- strawberry

- ice cream

- bread

- fish

- banana

Step 3: Find the intersection of sets
`\( M \)` and
`\( E \)` ,
`(\( M \cap E \)`).

This means we need to find items that are both human-made and edible. Looking at the lists from Step 1 and Step 2, we find there are no items that are both human-made and edible in the lists provided.

Therefore, based on the given sets
`\( M \)` and
`\( E \)`, there would be no elements in
`\( M \cap E \)`, which means the intersection of human-made and edible items is an empty set. None of the provided options in the question image would be selected since none are both human-made and edible.

Answer 2

Step1

write out the universal set

Step2

List out the subset of set M and set E

M= {X: x is human-made }. This set contains those items that are made by human

E={Y:y is edible }, this contains those items that are edible

`E=\mleft\lbrace\text{strawberry,ice}-\text{cream,bread,chocolate cookies,fish, banana}\mright\rbrace`

Step3: Take the common element to the two set above

`M\cap E\text{ are those element common to the two sets above }`

Hence,we are taking those items that are made by humans and are edible

`M\cap E=\mleft\lbrace\text{ice}-\text{cream,bread,Chocolate Chip cookies }\mright\rbrace`

Therefore the elements that apply to set M n E are Bread, Ice-cream