A) \[A\cup B=N\]
B) The complement of \[(A\cup B)\] is an infinite set
C) \[A\cap B\] Must be a finite set
D) \[A\cap B\] Must be proper subset of \[\{{{m}^{6}}:m\in N\}\]
Correct Answer: A
Solution :
[a]Let \[A=\{{{n}^{2}}:n\in N\}\] and \[B=\{{{n}^{3}}:n\in N\}\] \[A=\{1,4,9,16,....\}\] And \[B=\{1,8,27,64,...\}\] Now, \[A\cap B=\{1\}\] which is a finite set. Also, \[A\cup B=\{1,\,\,4,\,\,8,\,\,9,\,\,27.....\}\] So, complement of \[A\cup B\] is infinite set. Hence, \[A\cup B\ne N\]
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