a) true b) true c) false d)true e)true f)true g)false
few points
1) contains means set has element .
2) set A is said to be proper subset of B , if there exist element of B that is not in set A.(A$\subset$ B)
NOW in option a, b,c ,d asking about lhs element contain in rhs side set ...
in option c , lhs itself is element $\left \{ \Phi \right \}$ but rhs has set so its false
in option e ) proper subset of rhs will be $\left \{ \Phi \right \}, \left \{ \left \{ \Phi \right \} \right \}$ so its true
similar f ) is true
for g) we have to find proper subset of $\left \{ \left \{ \Phi \right \},\left \{ \Phi \right \} \right \}= \left \{ \left \{ \Phi \right \} \right \}$
so lhs will never be propersubset its itself set ...