# Mathematics: Sets Relations Functions: Power Set and Universal Set

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## Power Set

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.