In a discussion all sets are cosidered to be the subset of big set . Such a big set of which all other sets under discussion are subsets is called the universal set. We normally use the symbol U for the universal sets.

Examples: A set of all students of a in a school could be a universal set, if we consider the different sets of students whose age is below 10 , equal to10 or below or equal to 12 and above 12.

The set of all numbers below 1000 is universal set , if we consider the sets of numbers divisibe by 2 and 3 and neither by 2 nor by 3 within 1000.

The universal set is the set of all elements that are considered in a specific theory. We'll note the universal set with U.

We'll choose as universal set: U = {6,7,8,9,15,16,17,18,20,21}.

We have to determine the sets:

M = {x / x are the multiple of 3}

N = {x / x are the multiple of 5}

The elements of M and N have to be chosen from the universal set U.

To determine M, we'll identify the multiples of 3 from U: {6,9,15,18,21}

M = {6,9,15,18,21}

To determine N, we'll identify the multiples of 5 from U: {15,20}.

N = {15,20}