Can someone explain this to me.
Determine if each conclusion is valid or invalid for the given statements.
a. Some expensive books are mystery books. All mystery books are interesting.
Conclusion: Some interesting books are expensive.
Valid or invalid.
b. Some teachers are smart.
Some nice people are smart.
Conclusion: Some teachers are nice people.
Valid or invalid
How about using Venn diagrams?
Draw two intersecting circles, label one "mystery books", the other " expensive books"
Now draw a circle, called "interesting", intersecting the expensive circle, but totally surrounding the mystery circle.
your conclusion was "Some interesting books are expensive"
Do you see an overlap in the 'interesting' and the 'expensive' circles??
To determine the validity of the conclusions, we can use Venn diagrams.
a. For the given statements "Some expensive books are mystery books" and "All mystery books are interesting," we can represent these statements as overlapping circles. Label one circle as "expensive books" and the other as "mystery books." We also have a circle called "interesting" which surrounds the mystery books circle and intersects with the expensive books circle.
Now, let's analyze the conclusion "Some interesting books are expensive." If we examine the Venn diagram, we can see that there is indeed an overlap between the "interesting" and "expensive" circles. This means that there are some books that fall within both categories. Therefore, the conclusion is valid.
b. The given statements do not provide any direct relationship between teachers, nice people, and smart people. We cannot represent these statements as overlapping circles since there is no mentioned correlation between the categories. Therefore, we cannot determine the validity or invalidity of the conclusion "Some teachers are nice people" using Venn diagrams since the information given does not establish a link between these categories.
In conclusion:
a. Conclusion: Some interesting books are expensive. - Valid.
b. Conclusion: Some teachers are nice people. - Unable to determine validity without further information.