Definition: Two sets and are said to be disjoint if where is defined to be the empty set, that is, a set which contains no elements and thus and are disjoint if they. Note that Derek is in both sets, and therefore, in their intersection. Definition: The union of two sets A and B, is the set of elements which are in A or in B or in. In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the Since sets with unions and intersections form a Boolean algebra.


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  • Union of Sets | Math Goodies
  • Union and Intersection
  • Calculating Unions & Intersections in Mathematical Sets
  • Sets and Venn Diagrams
  • Operations of Mathematical Sets
  • Intersection (set theory)

Let's look at union, intersection and complement using a Venn diagram. We're going to continue using set K and set T.

Below is what a Intersection and union of sets diagram showing the sets K and T looks like: Venn diagram of sets K and T Let's examine how the Venn diagram is created. There's a circle intersection and union of sets each set - one circle for set K and another circle for set T. You can see that we labeled the circles so we don't get them mixed up.

We only have two circles because we only have two sets, but you will also see Venn diagrams with more than two circles. The circles intersect because there are objects, or elements, in each set that are the same.

I hope you notice that television and couch are listed in the universal set, but not found in set K or set T.

Sets and Venn Diagrams

Even though we didn't use it in a set, we still need to show it. In all cases where this happens, we list it outside the circles but within the box or universe. To show union in a Venn diagram, we highlight the circle K intersection and union of sets circle T: Highlighting sets in a Venn diagram shows union.

The set consisting of the objects in one set, say R, but not the other, S, is called the difference of sets and is denoted as R - S. In our example, all of the clothes in the world would be the universal set. Category 2 consists of clothing intersection and union of sets one set but not the other, so would be L - A or A - L.


These diagrams give us a visual representation of sets and allow us to more easily calculate unions, intersections, and differences. To illustrate a Venn diagram, let's use an example.

Suppose we have a universal set of the following numbers: The intersection of two sets would be where their circles intersect. The union of two sets would be everything in either of their circles.

Using this intersection and union of sets, we can place each of the elements in the universal set in the appropriate area. For example, consider the numbers 1, 2, and 4. And casey, drew and jade play Tennis: We can show that in a "Venn Diagram": Union of 2 Sets A Venn Diagram is clever because it shows lots of information: Do you see that alex, casey, drew and hunter are in the "Soccer" set?


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