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The diagram shows the number of children who have ever used motorized scooters, manual scooters, and/or bicycles.



Which combination represents the empty set?

motor ⋃ manual
motor ⋃ bicycle
motor ∩ manual
motor ∩ bicycle

The diagram shows the number of children who have ever used motorized scooters manual scooters andor bicycles Which combination represents the empty set motor m class=
The diagram shows the number of children who have ever used motorized scooters manual scooters andor bicycles Which combination represents the empty set motor m class=

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ANSWER

motor ∩ bicycle

EXPLANATION

The ∩ symbol represents the intersection, that is, A ∩ B is the set containing the elements that are in BOTH A and B.

motor ∩ bicycle means the intersection of two sets: motor and bicycle.

The intersection motor ∩ bicycle is a set that contains all elements that are in the motor set that are also in the bicycle set.

According to the Venn diagram, there are no items in the motor set that are also in the bicycle set. (If there were common elements to both sets, then there would be a Venn diagram overlap)

Therefore, motor ∩ bicycle = ∅, where ∅ is the empty set

The combination that represents the empty set is given by: Option D: motor ∩ bicycle

What is empty set?

Empty set is a set which doesn't contain any element.

When two sets have no intersection, then their intersection's result can be equated with empty set as we didn't got any common element.

We represent empty set with either [tex]\phi[/tex] or [tex]\{ \}[/tex]

We see that motor and manual have 24 elements in their intersection.

But motor and bicycle have 0 elements common, and so as for manual and bicycle.

Thus, symbolically we write:

  • motor ∩ bicycle = ∅
  • manual ∩ bicycle = ∅

Out of these two, only one of them is available (it is as option D).

Option A and B are not empty because union of a non-empty set with any set is non-empty.

Option C is false because motor and manual have 24 elements in their intersection.

Thus, the combination that represents the empty set is given by: Option D: motor ∩ bicycle

Learn more about empty set here:

https://brainly.com/question/14691345

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