| I. If A is a subset of the universal set U then its complement A? is also a subset of U. |
| II. If \[U=\{1,2,3,....,10\}\] and \[A=\{1,3,5,7,9\}\]then \[{{(A')}^{'}}=A.\] |
A) Only I is true
B) Only II is true
C) Both I and II are true
D) None of these
Correct Answer: C
Solution :
[c]If A is a subset of the universal set U, then its complement A? is also a subset of U. We have, \[A'=\{2,\,\,4,\,\,6,\,\,8,\,\,10\}\] Hence, \[(A')'=\{x:x\in U\,\,and\,\,x\notin A'\}=\{1,3,5,7,9\}=A\] It is clear from the definition of the complement that for any subset of the universal set U, we have \[(A')'=A\]
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