Question

The elements of the set \(\{x : x \text{ is an integer},\; x^2 \le 4\}\) can be represented as \(\ldots Z \ldots\). Here, \(Z\) refers to:

• A. \(\{-2, 2\}\)
• B. \(\{-1, 0, 1\}\)
• C. \(\{-2, -1, 0, 1, 2\}\)
• D. \(\{0, 1, 2\}\)

Hint:

When solving inequalities involving squares, always remember that both positive and negative values satisfy the condition (e.g., (x^2 = 4 Rightarrow x = pm 2)).

Answer 1

The Correct Option is C

Step 1: Understand the given condition. The set is defined as: \[ \{x : x \text{ is an integer and } x^2 \le 4\} \] Step 2: Solve the inequality. \[ x^2 \le 4 \Rightarrow -2 \le x \le 2 \] Step 3: List all integers satisfying the condition. The integers between \(-2\) and \(2\), inclusive, are: \[ -2,\; -1,\; 0,\; 1,\; 2 \] Step 4: Write the set in roster form. \[ Z = \{-2, -1, 0, 1, 2\} \] Thus, the correct option is \(\boxed{\{-2, -1, 0, 1, 2\}}\).