This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To find the intersection of sets A and B, we first need to determine the elements of set A. Step 1: Determine the elements of set A. Set A is defined as \x 1 ≤ x^2 < 9\. This inequality can be broken down into two parts: 1) 1 ≤ x^2 2) x^2 < 9 For 1 ≤ x^2: Taking the square root of both sides, we get sqrt(1) ≤ sqrt(x^2), which simplifies to 1 ≤ |x|. This means x ≤ -1 or x ≥ 1. For x^2 < 9: Taking the square root of both sides, we get sqrt(x^2) < sqrt(9), which simplifies to |x| < 3. This means -3 < x < 3. Combining these conditions, we need x such that (x ≤ -1 or x ≥ 1) AND (-3 < x < 3). The values of x that satisfy both conditions are: -3 < x ≤ -1 or 1 ≤ x < 3. Step 2: Identify the integer elements of set A. Since set B consists of integers and the options are sets of integers, we assume x must be an integer. For the interval -3 < x ≤ -1, the integers are \-2, -1\. For the interval 1 ≤ x < 3, the integers are \1, 2\. So, the integer elements of set A are A = \-2, -1, 1, 2\. Step 3: Find the intersection of set A and set B. Set A = \-2, -1, 1, 2\ Set B = \0, 1, 2, 3, 4\ The intersection A B consists of elements that are present in both sets. Comparing the elements, we find that 1 and 2 are common to both sets. Therefore, A B = \1, 2\. Step 4: Select the correct option. The calculated intersection is \1, 2\, which corresponds to option B. The final answer is B. \1, 2\. Send me the next one 📸