The "either reading or sports" should be interpreted as the exclusive or, not the inclusive or. IOW, the ones who like reading don't like sports, and the ones who like sports don't like reading. Without the word "either" it would be reasonable to assume that some like both activities.MarkFL said:I agree with your Venn diagram, and I guess it just boils down to how we interpret "like either reading or sports." It we take that to mean likes one or the other, but not both, then it is 55, but if we take it to mean likes at least one of the two, then it is 70.
Mark44 said:
In Logic and in Probability the word "or" (almost always) means "inclusive or", so "A or B" normally means "A or B or both". In set language this would be ##A \cup B##, while "A or B but not both" would be ##(A-B) \cup (B-A) = A \cup B - A \cap B##.tzx9633 said:
Thanks for the point !Ray Vickson said:
I agree with what you said regarding "A or B," but most of the cases I've seen with "either A or B," the intended meaning is one of the two alternatives, but not both. I can't cite any authoritative mathematical sources for this, but the Merriam-Webster dictionary defines "either-or" as "an unavoidable choice or exclusive division between only two alternatives".Ray Vickson said:
Mark44 said:
A Venn diagram is a visual representation of mathematical or logical relationships between different sets of objects. It consists of overlapping circles or other shapes that represent the sets, and the overlapping regions indicate the shared elements between the sets.
To read a Venn diagram, start by identifying the sets represented by each circle or shape. Then, look at the overlapping regions to determine the shared elements between the sets. The elements outside of the circles or shapes represent elements that are not included in either set.
To solve a Venn diagram problem, first identify the sets involved and the information given about each set. Then, use this information to fill in the appropriate regions of the diagram. Finally, use the diagram to answer the specific question being asked.
Venn diagrams are useful for visually organizing and understanding relationships between different sets of data or information. They can also be used to identify similarities and differences between sets, and to solve mathematical or logical problems.
Yes, a Venn diagram can have more than three sets. However, as the number of sets increases, the diagram can become more complex and difficult to read. In these cases, it may be helpful to use other types of visual aids, such as tables or charts, to represent the relationships between the sets.
