A) B is a proper non-empty subset of A
B) A and 8 are non-empty disjoint sets
C) \[B=\phi \]
D) None of the above
Correct Answer: C
Solution :
| [c] \[A=(A-B)\cup (B-A)\] ...(i) \[=(A\cap B)\cup (B\cap A')\] \[=\{(A\cap B)\cup B\}\cap \{(A\cap B')\cup A'\}\] \[=\{(A\cup B)\cap (B'\cap B)\}\cap \{(A\cup A')\cap (B'\cup A')\}\] \[=\{(A\cup B)\cap U\}\cap \{U\cap (B'\cup A')\}\] \[=(A\cup B)\cap (B'\cup A')\] \[=(A\cup B)\cap (A\cap B)'=\phi \]or \[A=\phi \] Here, \[B=\phi \]satisfy condition (i). \[\Rightarrow \] \[(A-\phi )\cup (\phi -A)=A\] \[\Rightarrow \] \[A\cup \phi =A\] \[\Rightarrow \] \[A=A\] |
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