Relations and Functions
Cartesian Product
Let A = {1, 2} and B = {4, 5, 6}
A × B = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6)}
Relations
A relation from a set 𝐴 to a set 𝐵 is a subset of 𝐴×𝐵 . Hence, a relation 𝑅 consists
∈ ∈ ∈
of ordered pairs (𝑎,𝑏) , where 𝑎 𝐴 and 𝑏 𝐵 . If (𝑎,𝑏) 𝑅 , we say that is related
to , and we also write 𝑎𝑅𝑏 .
Matrix Representation of a Relation
Let P = {1, 2, 3, 4}, Q = {a, b, c, d} and R = {(1, a), (1, b), (1, c), (2, b), (2, c), (2, d)}.
Relations and Functions 1
, Graph representation of a relation
Inverse Relation or converse relation
R-1 = {(y, x): y ∈ B and x ∈ A}.
Relations and Functions 2
Relations and Functions
Cartesian Product
Let A = {1, 2} and B = {4, 5, 6}
A × B = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6)}
Relations
A relation from a set 𝐴 to a set 𝐵 is a subset of 𝐴×𝐵 . Hence, a relation 𝑅 consists
∈ ∈ ∈
of ordered pairs (𝑎,𝑏) , where 𝑎 𝐴 and 𝑏 𝐵 . If (𝑎,𝑏) 𝑅 , we say that is related
to , and we also write 𝑎𝑅𝑏 .
Matrix Representation of a Relation
Let P = {1, 2, 3, 4}, Q = {a, b, c, d} and R = {(1, a), (1, b), (1, c), (2, b), (2, c), (2, d)}.
Relations and Functions 1
, Graph representation of a relation
Inverse Relation or converse relation
R-1 = {(y, x): y ∈ B and x ∈ A}.
Relations and Functions 2
