For the given statement identify the necessary condition
p : If a function is even then it will be symmetric about y -axis

Options

A. Function is even
B. Symmetric about y-axis.
C. Function is not even
D. Function does not exist

Answer

To solve the problem of identifying the necessary condition from the statement "If a function is even, then it will be symmetric about the y-axis," we can follow these steps:

### Step 1: Identify the structure of the statement
The given statement can be recognized as a conditional statement of the form "If p, then q," where:
- \( p \): A function is even.
- \( q \): The function is symmetric about the y-axis.

### Step 2: Understand the terms
In a conditional statement:
- The part before "then" (p) is known as the **sufficient condition**.
- The part after "then" (q) is known as the **necessary condition**.

### Step 3: Identify the necessary condition
From our identification in Step 1:
- The necessary condition (q) is that the function is symmetric about the y-axis.

### Step 4: Conclusion
Thus, the necessary condition for the given statement is:
- **The function is symmetric about the y-axis.**

### Final Answer
The necessary condition is: **The function is symmetric about the y-axis.**

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