describe the venn diagram for two disjoint sets. how does this diagram illustrate that the sets have no common elements?
... im a bit confused, because to me, if the sets are disjoint and hence nothing is in common, it wouldnt be a venn diagram in the first place because you wouldnt be able to put anything in the center. ??
if anyone can clarify this, id be very grateful =)
disjoint sets? The venn diagram is two circles, sitting side by side, with no overlapping area.
... oh, thank you for that clarification =D
When two sets are disjoint, it means that they have no elements in common. You are correct in thinking that in a traditional Venn diagram, where overlapping regions represent common elements, there would be no overlap if the sets are disjoint.
To clarify, a Venn diagram can still be used to represent two disjoint sets. In this case, there would be two separate circles (or shapes) representing the two sets, and these circles would not overlap at all. The absence of an overlapping region indicates that there are no common elements between the sets.
So, even though the Venn diagram may not have any elements in the center, it can still be used to visualize the concept of disjoint sets by showing the separation and lack of shared elements between the two sets.
I can understand why you might find it confusing, but let me explain it in detail. A Venn diagram is a visual representation of sets using circles or other shapes. The purpose of a Venn diagram is to show the relationships between different sets.
In the case of two disjoint sets, it means that the two sets have no elements in common. So, when representing this in a Venn diagram, the circles representing the sets would not overlap at all. There would be no area where the circles intersect.
To illustrate this, you would draw two separate circles that do not overlap at all. Each circle represents one of the disjoint sets. The absence of any overlapping area visually demonstrates that there are no elements that belong to both sets.
Keeping the circles separate in the Venn diagram is crucial to show that the sets have no common elements. This way, you can clearly see that the circles do not touch or overlap, indicating that the sets are completely distinct and have no elements in common.
So, while it might initially seem odd to represent sets with no common elements in a Venn diagram, it can still be done to visually demonstrate that these sets are disjoint.