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 .

Power set

Power Set

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.

Universal Set

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.

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