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Set Operation: Intersection - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

A set operation is the collection of two data sets. Types of set operations include union, intersections and complements. Intersection set operations is a new set of data that is constructed by determining the values that two sets have in common. For example, the intersection of data set A and data set B is the set of all things which members of both A and B.

Set operations intersection, so an intersection is a combination of two sets of information and the way I always think about it is sort of the intersection of two streets okay? When you talk about the intersection that's really where those two things come together okay? In two roads wherever they're coming from doesn't matter wherever they're going doesn't matter but the intersect themselves is just what those two things have in common okay? Same exact idea comes into effect with numbers okay? So let's look here, here we have a bunch of sets each with four different numbers so a is a couple of even numbers b is a couple odd and c is just some numbers in the middle and intersection always always designated by this upside down u okay?
And so what we're looking for in this example is the intersection of a and c, we're looking for numbers that are in both a and c in that intersection there, so if you look at it say okay a has a number 2 but c doesn't so therefore it's not in the intersection. a has a number 4, 4 is in c so therefore that is in that intersection so we can include 4 okay? Going down [IB] 6, 6 is in a, 6 is in c so that is in the intersection as well, 8 is in a not in c so it's not in the intersection okay? Those are really the only numbers that are in there because we have c has the numbers 3 and 5 but we only determine those aren't in a so they cannot be intersection as well, so the intersection of a and c are just the numbers 4 and 6 okay?
Let's look at another example, say the intersection of a and b, so here we're looking for the numbers that a and b have in common. Beginning we said that a is even and b is odd, so is there any way for these two sets to share anything? No, because they're completely different numbers, so what you may see is different ways of writing this. You can either see what they call the open set, which is just basically two brackets but nothing in it or you may also see an all set circle with a cross through it. Two different ways of writing the exact same thing.
Another way your teacher may describe intersection is with the Venn diagram okay? Let's say we have two sets of data a and b, the intersection is what these two share so where these two actually overlap, in this case a is everything over here, b is everything over here what they share is just this little teeny slither in the middle okay? So another way of looking at it what these two sets share is what it's in that middle right there and there is intersection.

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