Is it necessary for an element to be kept in braces if we want to separate it from a set and make the element subset of the same set? Like in...
$$A= \{a,b,c\}$$
If we want to make the element $a$ above a subset of $A$, is it then necessary to take out a from A and write it separately as $\{a\}.$
Yes, in order to show the elements of the set, you put the elements in braces and use the symbol $\subset$.
For example $$\{ 2,4,6,8,10\} \subset \{1,2,3,4,5,6,7,8,9,10\}$$ means that $$\{ 2,4,6,8,10\}$$ is a subset of $$\{1,2,3,4,5,6,7,8,9,10\}$$