Equal sets
Two sets A and B are said to be equal if they have exactly the same elements and we write A = B.
Otherwise, the sets are said to be unequal and we write A ≠ B.
Examples: Let A = { 1, 2, 3, 4 } and B = { 3, 1, 4, 2 }. Then A = B. Let C = { 1, 2, 3, 4 } and D = { 1,2,3,5 }. Then C ≠ D.
If set A = { 1, 2, 3 } and B = { 2, 2, 1, 3, 3 }. Then A = B, since each element of A is in B and vice-versa. That is why we generally do not repeat any element in describing a set.
Sub sets
A set A is said to be a subset of a set B if every element of A is also an element of B.
Consider set A = set of all students in your class, B = set of all students in your School. We note that every element of A is also an element of B; we say that A is a subset of B.
A is subset of B is expressed in symbols as A ⊂ B. The symbol ⊂ stands for‘ is a subset of’ or‘ is contained in’.
It follows from the above definition that every set A is a subset of itself, i. e. A ⊂ A.
Since the empty set φ has no elements, we agree to say that φ is a subset of every set.