The negation of the statement A circle is an ellipse " is

Options

A. A. An ellipse is a circle
B. B. A circle is not an ellipse
C. C. An ellipse is not a circle
D. D. none of these

Answer

To find the negation of the statement "A circle is an ellipse," we need to follow a systematic approach to understand how negation works in logical statements.

### Step-by-Step Solution:

1. **Identify the Original Statement:**
The original statement is "A circle is an ellipse." This is a positive statement asserting a relationship between circles and ellipses.

2. **Understand Negation:**
The negation of a statement reverses its truth value. If the original statement is true, the negation will be false, and vice versa. For a statement of the form "P is Q," the negation is "P is not Q."

3. **Apply Negation to the Statement:**
Applying the negation rule to our statement:
- The original statement: "A circle is an ellipse."
- The negation becomes: "A circle is not an ellipse."

4. **Check the Options Provided:**
Now, we check the options given in the question:
- a) An ellipse is a circle
- b) A circle is not an ellipse
- c) An ellipse is not a circle
- d) None of these

From our negation, we see that option b) "A circle is not an ellipse" matches our derived negation.

5. **Conclusion:**
Therefore, the negation of the statement "A circle is an ellipse" is "A circle is not an ellipse," which corresponds to option b.

### Final Answer:
The negation of the statement "A circle is an ellipse" is **"A circle is not an ellipse."**

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