Step 1: Understanding the Question:
This is a Syllogism problem, a core part of deductive reasoning. In these problems, we are given certain premises and must find a conclusion that is 100 percent logically certain based on those premises. We must treat the statements as absolutely true, regardless of real-world facts. The goal is to identify the relationship between three sets: Tablets, Desktops, and Computers, specifically focusing on how the lack of overlap between the first two affects the third.
Step 2: Key Formulas and approach:
The most effective approach is the "Venn Diagram Method."
1. Draw a circle for Tablets and a circle for Desktops. Since the statement says "No tablets are desktops," these two circles must not touch or overlap at all.
2. Draw a circle for Computers. Since "Some computers are tablets," the Computer circle must overlap with the Tablet circle.
3. A conclusion is valid only if it is true in every possible way you can draw the circles while still following the rules.
Step 3: Detailed Explanation:
We start with the first rule: Tablets and Desktops are entirely separate sets. If an object is a tablet, it is guaranteed not to be a desktop.
The second rule tells us there is an intersection between Computers and Tablets. This means there is a group of items that are both computers and tablets at the same time.
Let's look at that specific intersection—the "Computers that are Tablets."
Because these items are tablets, and we know that no tablets can be desktops, it logically follows that these specific computers can never be desktops.
This proves that at least "some" computers (the ones that are tablets) are definitively "not desktops."
Let's check Option A: "Some computers are desktops." This might be true if the computer circle also overlaps with the desktop circle, but it's not guaranteed.
Let's check Option D: "No desktops are computers." We can't say this for sure because there might be desktops that are also computers outside of the tablet category.
Option B is the only one that must be true in every possible diagram.
Step 4: Final Answer:
The logically valid conclusion is that some computers are not desktops.