Write negation of the statement: “There exists a complex
number which is not a real Number”

Answer

To find the negation of the statement “There exists a complex number which is not a real number,” we will follow these steps:

### Step 1: Identify the original statement
The original statement is: “There exists a complex number which is not a real number.”

### Step 2: Understand the quantifiers
The phrase “There exists” indicates the use of the existential quantifier (∃). This means that at least one complex number does not belong to the set of real numbers.

### Step 3: Apply the negation
The negation of an existential quantifier (∃) is a universal quantifier (∀). Therefore, the negation of “There exists” becomes “For all.”

### Step 4: Rewrite the statement with the negation
Now we need to negate the inner part of the statement. The original statement says that there exists a complex number that is not a real number. The negation of “not a real number” is “is a real number.”

### Step 5: Combine the negation
Putting it all together, we get: “For all complex numbers, they are real numbers.”

### Final Answer
The negation of the statement “There exists a complex number which is not a real number” is:
**“For all complex numbers, they are real numbers.”**

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