Is A⊆ A? All elements of LHS set A are also elements of RHS set A. Thus …

Thus, Q' = {x : x ∈ R and x ∉ Q} i.e., all real numbers that are not rational. eg.√2 , √5 and & π

Similarly, the set of natural numbers, N is a subset of the set of whole numbers W and we can write N ⊂ W. Also W is a subet of ¡

That is.        N ⊂ W and W ⊂ R

Some of the obvious relations among these subsets are N ⊂ Z ⊂Q R and Q' ⊂R and N ⊄ Q'.

onsider the set of vowels, V = {a, e, i, o, u}. Also consider the set A, of all letters in the English alphabet. A = {a, b, c, d, ….., z}. We can see that every element of set V is also an element A. But there are elements of A which are not a part of V. In this case, V is called the proper subset of A.

In other words V ⊂ A since, whenever a ∈ V, then a ∈ A It can also be denoted by V ⊆ A and is read as V is the subset of A.