Question

If all Bloops are Razzies and some Razzies are Lazzies, which of the following is definitely true?

• A. All Bloops are Lazzies
• B. Some Bloops are Lazzies
• C. Some Razzies are Bloops
• D. No Bloops are Lazzies

Hint:

For logical reasoning problems involving sets, draw a Venn diagram to represent the relationships between categories. Focus on what must be true based on the given statements, and test each option by considering whether it is always true or only sometimes true. Avoid assuming additional relationships not explicitly stated.

Answer 1

The Correct Option is C

Let’s break down the statements using logical reasoning and visualize the relationships:

• Statement 1: All Bloops are Razzies. This means the set of Bloops is entirely contained within the set of Razzies. In other words, every Bloop is also a Razzie, but there may be Razzies that are not Bloops.
• Statement 2: Some Razzies are Lazzies. This means there exists at least one Razzie that is also a Lazzie, so the sets of Razzies and Lazzies overlap.

Now, let’s evaluate each option:

• (1) All Bloops are Lazzies: This is not necessarily true. While some Razzies are Lazzies, the Bloops (which are all Razzies) may or may not be in the overlapping section of Razzies and Lazzies. For example, the Bloops could be Razzies that are not Lazzies.
• (2) Some Bloops are Lazzies: This is also not necessarily true. It’s possible that the Razzies that are Lazzies do not include any Bloops. The statement only guarantees that some Razzies are Lazzies, but those Razzies could be outside the Bloop set.
• (3) Some Razzies are Bloops: This is definitely true. Since all Bloops are Razzies, there must be some Razzies that are Bloops (as long as there is at least one Bloop). This follows directly from the first statement.
• (4) No Bloops are Lazzies: This is not necessarily true. It’s possible that some Bloops are Lazzies if the Bloops fall in the overlapping section of Razzies and Lazzies, but it’s also possible that no Bloops are Lazzies.

Understand with the help of a Venn diagram:

The overlap between Razzies and Lazzies may or may not include the Bloops circle, making options (1), (2), and (4) uncertain. However, since Bloops are inside Razzies, there are always some Razzies that are Bloops, confirming option (3).
Thus, the only statement that is definitely true is (3).