A) \[\phi \subseteq A,\phi \in A,\{\phi \}\in A,\{\phi \}\subseteq A\]is true
B) \[\phi \in A\]but\[\phi \underline{\not\subset }A\]
C) \[\{\phi \}\in A\]but\[\phi \,\underline{\not\subset }\,A\]
D) A is a null set
Correct Answer: A
Solution :
The given set is \[A=\{\phi ,\{\phi \},\{\phi ,\{\phi \}\}\}\] Since empty set is a subset of every set \[\therefore \] \[\phi \subseteq A\] Also, \[\phi \] is an element of the given set A \[\Rightarrow \] \[\phi \in A\]. Now, since \[\{\phi \}\] is an element of the set A \[\Rightarrow \] \[\{\phi \}\in A\] Also \[\{\phi \}\] is a subset of A being an element of a set A. \[\therefore \] \[\{\phi \}\subseteq A\] So, correct option is [a].
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