If A and B are non-empty subsets of a set, and A^{c} and B^{c} represent their complements, then which of the following is/are correct? I. A-B=B^{c}-A^{c} II. A-B^{c}=A^{c}-B Select the answer using the code given below.
- A. I only ✓
- B. II only
- C. Both I and II
- D. Neither I nor II
Correct Answer: A. I only
Explanation
For I: A - B = A \cap B^c. Also, B^c - A^c = B^c \cap (A^c)^c = B^c \cap A = A \cap B^c. So, I is correct. For II: A - B^c = A \cap (B^c)^c = A \cap B, whereas A^c - B = A^c \cap B^c = (A \cup B)^c. They are generally not equal. Hence, only statement I is correct.
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