How do you represent sets using a Venn diagram?

You represent sets using a Venn diagram by drawing circles that overlap to show relationships between the sets.

In a Venn diagram, each set is represented by a circle. The elements of the set are placed inside the circle. If two sets have common elements, their circles will overlap, and the common elements are placed in the overlapping region. For example, if Set A contains {1, 2, 3} and Set B contains {3, 4, 5}, the number 3 will be in the overlapping area of the circles representing Set A and Set B.

The area where the circles overlap is called the intersection of the sets. This intersection shows the elements that are common to both sets. In our example, the intersection of Set A and Set B is {3}. If there are elements that belong to only one set and not the other, they are placed in the non-overlapping parts of the circles. For instance, 1 and 2 will be in the part of Set A's circle that does not overlap with Set B, and 4 and 5 will be in the part of Set B's circle that does not overlap with Set A.

If there are more than two sets, you can add more circles to the Venn diagram. The overlapping regions will then show the common elements among all the sets. For three sets, the diagram will have seven distinct regions: one for each set individually, three for the pairwise intersections, and one for the intersection of all three sets. This helps to visually analyse the relationships and shared elements among multiple sets.