Question

Statements:
No tablets are desktops.
Some computers are tablets.
Conclusion?

• A. Some computers are desktops.
• B. Some computers are not desktops.
• C. All computers are desktops.
• D. No desktops are computers.

Hint:

When dealing with syllogisms, a conclusion is only true if it holds true in every possible Venn diagram you can draw that satisfies the statements.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This is a logical reasoning problem based on syllogism. We need to determine which provided conclusion logically and definitively follows from the given two statements.


Step 2: Detailed Explanation:
Let's thoroughly analyze the given statements using set theory concepts (or Venn diagrams).
1. "No tablets are desktops" logically means that the set of Tablets (\( T \)) and the set of Desktops (\( D \)) are completely disjoint. There is absolutely no intersection between them (\( T \cap D = \emptyset \)).
2. "Some computers are tablets" means there is a definite intersection between the set of Computers (\( C \)) and the set of Tablets (\( T \)). At least some elements exist that are simultaneously both computers and tablets.
Now let's evaluate the inevitable outcome:
Because some computers are firmly within the tablet set, and absolutely no tablets can ever be desktops, those specific computers which are tablets can never be desktops.
Therefore, it logically follows that there is at least a portion of the computer set that falls entirely outside the desktop set boundaries.
This makes the conclusion "Some computers are not desktops" definitively and undeniably true.
Let's quickly check why the other options fail:
- (A) Some computers are desktops: This is merely a possibility, but not a definite conclusion guaranteed by the statements.
- (C) All computers are desktops: This directly contradicts our proven conclusion that some are not.
- (D) No desktops are computers: We don't have enough restricting information to conclude this; some computers outside the tablet circle might still intersect with the desktop circle.


Step 3: Final Answer:
The correct conclusion is "Some computers are not desktops."