Question

Consider the following sets: \[ A = \{"this", "that"\}, \quad B = \{"that", "other"\}, \quad C = \{"other", "this"\} \] 

 Which of the following sets remain non-empty at the end?

• A. Only A
• B. A and C
• C. Only C
• D. Only B

Hint:

Set operations such as union (\(|\)), difference (\(-\)), and intersection are crucial in programming logic and mathematical problem-solving.

Answer 1

The Correct Option is C

Step-by-step execution: 1. Initial Condition: \[ A = \{"this", "that"\}, \quad B = \{"that", "other"\}, \quad C = \{"other", "this"\} \] 2. First Iteration (`while "other" in C`) - `"this"` is in \( A \), so we update: \[ A = A - B = \{"this", "that"\} - \{"that", "other"\} = \{"this"\} \] \[ B = B - C = \{"that", "other"\} - \{"other", "this"\} = \{"that"\} \] \[ C = C - A = \{"other", "this"\} - \{"this"\} = \{"other"\} \] 3. Second Iteration (`while "other" in C`) - `"this"` is still in \( A \), so we update: \[ A = A - B = \{"this"\} - \{"that"\} = \{"this"\} \] \[ B = B - C = \{"that"\} - \{"other"\} = \{"that"\} \] \[ C = C - A = \{"other"\} - \{"this"\} = \{"other"\} \] 4. Termination Condition - The second condition `"that" in B"` leads to: \[ A = C - A = \{"other"\} - \{"this"\} = \{"other"\} \] \[ B = A | B = \{"this"\} | \{"that"\} = \{"this", "that"\} \] \[ C = B | C = \{"that"\} | \{"other"\} = \{"that", "other"\} \] Thus, the only set remaining non-empty at the end is C. Conclusion: The correct answer is (3) Only C.