Definitions of set, sub-set, proper sub-set

SETS: A collection of well defined objects is called a set. It is always represented by a capital letter. A set can be represented by
(i) a venn diagram (ii) an equation or an expression or (iii) verbal expression.

1. A set can be represented by a closed figure like a circle, a triangle etc. Such a representation is called a Venn diagram.
   The points inside this figure represent the members of the set.
2. If a set A contains objects having property P in common, we write the
   set A ≡ {x / x has property P}
   If B ≡{3, 4} ≡ {x / x ∈ W and x² - 7x + 12 = 0}.
   If C ≡ {7, 8, 9, 10, ...} ≡ {x / x ∈ W, x ≥ 7.
   This is also known as the set builder notation.
3. If a set A is set of all vowels in English alphabets, then A ≡ {a, e, i, o, u}.
   A ≡ {set of all vowels in English alphabets}
   
   This is verbally expressed