Power Set:
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NIOS Mathematics Part 1 Ch 1 Sets Relations Functions Part 4
Let then, Subset of are and . If we consider these subsets as elements of a new set (say) then, . is said to be the power set of .
Example:
Write the power set of each of the following sets:
(i)
(ii)
Solution:

Clearly (Null set), is the only subset of given set,

The set can be written as

Subsets of are

.
Universal Set:
A Universal Set is the set of all elements under consider, denoted by capital . All other sets are subsets of the universal set.
Example:
Which of the following sets can be considered as a universal set?
Solution:

As it is clear that both sets and are subset of .

is the universal set for this problem.