Consider the 3 statements below to be true
All insects that are attracted to honey are ants.
Insect I is not an ant.
Insect J is attracted to honey.
Which of the following statement is necessarily true?

Options

A. Insect I is ant not attracted to honey
B. Insect I is an ant attracted to honey
C. Insert I is attracted to honey
D. Insert J is an ant

Answer

To solve the problem, we need to analyze the three statements provided and determine which conclusion is necessarily true based on the information given.

### Step 1: Understand the Statements
1. **Statement 1**: All insects that are attracted to honey are ants.
2. **Statement 2**: Insect I is not an ant.
3. **Statement 3**: Insect J is attracted to honey.

### Step 2: Analyze the Implications
From Statement 1, we can infer that if an insect is attracted to honey, it must be an ant. This means that the set of all insects attracted to honey is a subset of the set of ants.

### Step 3: Visualize with a Venn Diagram
- Draw a large circle representing all ants.
- Inside this circle, draw a smaller circle representing all insects attracted to honey.
- Since Insect I is not an ant (Statement 2), it must lie outside the large circle.
- Since Insect J is attracted to honey (Statement 3), it must lie inside the smaller circle, which means it is also inside the larger circle (the set of ants).

### Step 4: Evaluate Each Option
Now we will evaluate each of the provided options to see which one is necessarily true:

- **Option A**: "Insect I is an ant not attracted to honey."
- This cannot be true because Insect I is not an ant (Statement 2).

- **Option B**: "Insect I is an ant attracted to honey."
- This is also false because Insect I is not an ant.

- **Option C**: "Insect I is attracted to honey."
- This cannot be true because if Insect I were attracted to honey, it would have to be an ant (from Statement 1), contradicting Statement 2.

- **Option D**: "Insect J is an ant."
- This is true because Insect J is attracted to honey, and according to Statement 1, all insects attracted to honey are ants.

### Conclusion
The only statement that is necessarily true based on the given information is **Option D**: "Insect J is an ant."

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