Determine whether the argument used to check the validity of the following statement is correct.
p `: ` If `x^(2)` is irrational , then x is rational. The statement is true because:- Number `x^2=pi^2` is irrational therefore `x=pi` irrational.

Answer

To determine whether the argument used to check the validity of the statement "If \( x^2 \) is irrational, then \( x \) is rational" is correct, we will analyze the statement and the argument step by step.

### Step 1: Understand the statement
The statement we are analyzing is:
- **Statement \( p \)**: If \( x^2 \) is irrational, then \( x \) is rational.

### Step 2: Analyze the argument
The argument provided states:
- If \( x^2 = \pi^2 \) (which is irrational), then \( x = \pi \) (which is also irrational).

### Step 3: Identify the logical flaw
The argument attempts to prove that the statement \( p \) is true by providing a counterexample. However, it actually shows that:
- If \( x^2 \) is irrational, it does not necessarily follow that \( x \) is rational. In fact, the example given shows that \( x \) can be irrational (since \( \pi \) is irrational).

### Step 4: Conclusion
Since the argument shows that \( x^2 \) being irrational can lead to \( x \) being irrational, it contradicts the original statement \( p \). Therefore, the argument used to check the validity of the statement is incorrect.

### Final Answer
The argument used to check the validity of the statement "If \( x^2 \) is irrational, then \( x \) is rational" is false.

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