1. **Problem Statement:** Determine the truth or falsity of the following statements: - \( A = \{ x \in \mathbb{Z} \mid -2 \leq x < 5 \} = [-2,5) \) - The sequence \( \sqrt{3}, 2\sqrt{3}, 4\sqrt{3}, \ldots \) is an arithmetic sequence with common difference 3. - The angle 110 degrees lies in the third quadrant of the unit circle. - The set of molecules in a specific water molecule is a finite set. 2. **Step 1: Analyze the set \( A \)** - \( A = \{ x \in \mathbb{Z} \mid -2 \leq x < 5 \} \) means all integers \( x \) such that \( -2 \leq x < 5 \). - This set includes integers: \( -2, -1, 0, 1, 2, 3, 4 \). - The notation \( [-2,5) \) usually denotes a real interval including all real numbers \( x \) with \( -2 \leq x < 5 \). - Since \( A \) is a set of integers and \( [-2,5) \) is a set of real numbers, they are not equal. **Conclusion:** The statement is **false**. 3. **Step 2: Check if the sequence is arithmetic with common difference 3** - The sequence is \( \sqrt{3}, 2\sqrt{3}, 4\sqrt{3}, \ldots \). - Calculate the differences: - \( 2\sqrt{3} - \sqrt{3} = \sqrt{3} \) - \( 4\sqrt{3} - 2\sqrt{3} = 2\sqrt{3} \) - Differences are not constant, so it is not an arithmetic sequence. **Conclusion:** The statement is **false**. 4. **Step 3: Determine the quadrant of 110 degrees** - Quadrants are divided as: - 1st quadrant: \( 0^\circ < \theta < 90^\circ \) - 2nd quadrant: \( 90^\circ < \theta < 180^\circ \) - 3rd quadrant: \( 180^\circ < \theta < 270^\circ \) - 4th quadrant: \( 270^\circ < \theta < 360^\circ \) - Since \( 110^\circ \) lies between \( 90^\circ \) and \( 180^\circ \), it is in the **second quadrant**. **Conclusion:** The statement is **false**. 5. **Step 4: Is the set of molecules in a water molecule finite?** - A water molecule \( H_2O \) consists of 2 hydrogen atoms and 1 oxygen atom. - The set of molecules in a single water molecule is just one molecule. - A set with one element is finite. **Conclusion:** The statement is **true**. **Final answers:** - Statement 1: False - Statement 2: False - Statement 3: False - Statement 4: True