Are $\{\{a\},\{b,c\},\{d\},\{e\}\}$ and $\{a,b,c,d,e\} $ the same set? 
Are $A = \{\{a\},\{b,c\},\{d\},\{e\}\}$ and $B = \{a,b,c,d,e\} $the same set? Justify your answer.

I think I get that set $A$ has elements in the form of sets: $\{a\}, \{b,c\}, \{d\}$ and $\{e\}$. Is that the same as the elements in $B$?
Could someone explain if these two sets are the same or not? 
Thank you!
 A: Your question is in general shape ("are $A$ and $B$ the same set?") and the answer is: "no". 
To justify this it is enough to show that $5$ distinct sets exists and to label them as $a,b,c,d,e$. 
Then - as commented by @Joe - the set $A=\{\{a\},\{b,c\},\{d\},\{e\}\}$ has exactly $4$ elements and the set $B=\{a,b,c,d,e\}$ has exactly $5$ elements, so the sets are definitely not the same.
Another (specified) question would be: do sets $a,b,c,d,e$ exist such that $\{\{a\},\{b,c\},\{d\},\{e\}\}=\{a,b,c,d,e\}$? 
Then - if the axiom of regularity is accepted - again the answer is "no", but a proof of this is much less easy.
A: Two sets $A,B$ are equal iff for all $x$, $x\in A$ iff $x\in B$.
In your case $A$ elements $\{a\},\{b,c\},\{d\},\{e\}$ and $B$ has elements $a,b,c,d,e$.
But $a\ne \{a\}$ (but $a\in\{a\}$), the set $\{b,c\}$ has the elements $b,c$ and $d\ne\{d\}$, $e\ne\{e\}$. So they are far from being equal.
A: Two Reasons why it is not true. 
1) set A = contains 5 elements and Set B contains 4. 
For example, if you have a Set A = {{x,y,g,p}} set A only has one element which is the set of x,y,g, and p. Not every element in the set. 
2) If you compares the elements inside, a $\neq$ {a} . The set {a} also includes the empty set $\phi$. You will learn more on this when you study powers of sets. 
