Let A be the set of students who live within one mile of...

Let $A$ be the set of students who live within one mile of school and let $B$ be the set of students who walk to classes. Describe the students in each of these sets.
a) $A \cap B$
b) $A \cup B$
c) $A-B$
d) $B-A$

Key Concepts

Set Intersection

The set intersection of two sets refers to the collection of all elements that are common to both sets. In general, when considering two sets, the intersection contains only those elements that belong simultaneously to each of the sets, making it a fundamental operation for identifying shared attributes or membership between groups.

Set Union

The set union of two sets is the collection of all elements that belong to at least one of the sets. This concept consolidates all unique elements from both sets, ensuring that each element is represented only once regardless of whether it appears in one or both sets. It is crucial for comprehensively combining elements from distinct groups.

Set Difference

The set difference between two sets, denoted typically as A ? B or B ? A, is the operation that results in a set containing those elements that are present in the first set but not in the second. It is a key concept used to isolate elements that are exclusive to one set, thereby differentiating between overlapping and non-overlapping content within the sets.

Transcript

00:01 Once again, i welcome to new problem.

00:05 When you think about sets, so when you think about set, a set is a collection.

00:13 A set is a collection of elements.

00:16 So this is when you're thinking about sets and what tends to happen.

00:21 If i have a set a with a bunch of elements, say one, two, three, four, and five.

00:30 And then i also have another set b with a bunch of elements, one, two, three.

00:37 So b is going to be a subset of a, for example, b can be a subset of a.

00:45 And then also, if you think about two sets in b, a union b would be the union of two sets, and that involves the elements, the elements in both a and b.

01:08 So the elements in both a, not nb, but orb.

01:13 So that's pretty much all the elements.

01:15 And then if you have a intersection b, these are common elements, common elements in both a and b.

01:28 So the sets in b and then we could also have a minus b.

01:35 So these are elements that exist in a but not in b.

01:50 And then also a complement is all the elements, all the elements, all the elements not in so we have a new problem and in the problem we have a, these are the students, these are the students living within one mile of the school.

02:26 And then b is students walking to classes, students working to classes.

02:37 So in part a, we're saying what's a intersection b? so we want to describe all of these...

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