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Given the universal set = {-7, -3, -1, 0...

Given the universal set = {-7, -3, -1, 0, 5, 6, 8, 9}, find :
(i) `A={x: x lt 2}`, (ii) `B={x : -4 lt x lt 6}`

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The correct Answer is:
To solve the problem, we need to find the sets A and B based on the given conditions from the universal set. **Step 1: Identify the Universal Set** The universal set is given as: \[ U = \{-7, -3, -1, 0, 5, 6, 8, 9\} \] **Step 2: Define Set A** Set A is defined as: \[ A = \{x : x < 2\} \] This means we need to find all elements in the universal set that are less than 2. **Step 3: Find Elements for Set A** Now, we will check each element of the universal set: - \(-7 < 2\) (Include) - \(-3 < 2\) (Include) - \(-1 < 2\) (Include) - \(0 < 2\) (Include) - \(5 < 2\) (Do not include) - \(6 < 2\) (Do not include) - \(8 < 2\) (Do not include) - \(9 < 2\) (Do not include) Thus, the elements of set A are: \[ A = \{-7, -3, -1, 0\} \] **Step 4: Define Set B** Set B is defined as: \[ B = \{x : -4 < x < 6\} \] This means we need to find all elements in the universal set that are greater than -4 and less than 6. **Step 5: Find Elements for Set B** Now, we will check each element of the universal set: - \(-7 > -4\) (Do not include) - \(-3 > -4\) (Include) - \(-1 > -4\) (Include) - \(0 > -4\) (Include) - \(5 > -4\) (Include) - \(6 > -4\) (Do not include) - \(8 > -4\) (Do not include) - \(9 > -4\) (Do not include) Thus, the elements of set B are: \[ B = \{-3, -1, 0, 5\} \] **Final Result:** - Set A: \(\{-7, -3, -1, 0\}\) - Set B: \(\{-3, -1, 0, 5\}\) ---
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