i) Membership: The notation used to describe membership is the symbol "∈". This symbol is used to indicate that an element belongs to a set. For example, if we have a set A = {1, 2, 3}, we can say that 1 ∈ A, which means that 1 is an element of the set A.
ii) Subset: The notation used to describe subset is the symbol "⊆". This symbol is used to indicate that all the elements of one set are also elements of another set. For example, if we have two sets A = {1, 2, 3} and B = {1, 2, 3, 4}, we can say that A ⊆ B, which means that all the elements of set A are also present in set B.
iii) Equality of two sets: The notation used to describe equality of two sets is the symbol "=". This symbol is used to indicate that two sets have exactly the same elements. For example, if we have two sets A = {1, 2, 3} and B = {3, 2, 1}, we can say that A = B, which means that both sets have the same elements.
iv) Union: The notation used to describe union is the symbol "∪". This symbol is used to indicate that we combine two sets into a single set, with no duplicates. For example, if we have two sets A = {1, 2, 3} and B = {3, 4, 5}, we can say that A ∪ B = {1, 2, 3, 4, 5}. The mathematical expression for union is:
A ∪ B = {x | x ∈ A or x ∈ B}