# Universal, Mutually Exclusive & Disjoint Sets

UNIVERSAL SET:

A universal set is a set of all elements under consideration. It is denoted by U. A Universal set is always a non-empty set.

For example: The set of real numbers R is a universal set for the operations related to real numbers.

Example:

Given that U = {5, 6, 7, 8, 9, 10, 11, 12}, list the elements of the following sets.
• A = {x : x is a prime number}
• B = {x : x is a factor of 60}
Solution:

The elements of sets A and B can only be selected from the given universal set U
• A = {5, 7, 11}
• B = {5, 6, 10, 12}

MUTUALLY EXCLUSIVE SETS OR DISJOINT SETS:

Two sets are called disjoint if they don't have any common element.

For example, A = {2, 3, 4} and B = {5, 6, 7} are disjoint sets.

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