Q. What is set theory? Define universal set?

Ans.

The universe, or universal set, written as U, is the set that contains all elements being considered in a given discussion. For example, if we are considering the states in the U.S., the universe will contain 50 elements: California, Alaska, New York, etc. In set notation this is written:

It is read: "U is the set of all x such that x is a state of the U.S."

The elements of a set are all of the possible members of the set.

The cardinal number of a set is the number of elements in that set. This corresponds to the notation n(A), meaning the number of elements of set A.

A set that contains no elements has a cardinal number of 0 and is called the empty or null set, written as Φ or {}.

The set B is a subset of A, denoted B ⊆ A., if and only if every element of B is an element of A. Notice that this definition of subset allows B to be equal to A. Two subsets are equal if they have the exact same elements.

if B ⊆ A And A ⊆ B then A= B