RELATIONS AND FUNCTIONS

A relation R in a set A is called , if no element of A is related to any element of A, i.e., R = φ ⊂ A × A.

A relation R in a set A is called , if each element of A is related to every element of A, i.e., R = A × A.

A relation R in a set A is called , if (a, a) is an element of R, for every a is an element of A.

A relation R in a set A is called , if (a1, a2) is an element of R implies that (a2, a1) is an element of R, for all a1,a2 is an element of A.

A relation R in a set A is called , if (a1, a2) is an element of R and (a2, a3) is an element of R implies that (a1, a3)is an element of R, for all a1, a2,a3 is an element of A.

A relation R in a set A is said to be an if R is reflexive, symmetric and transitive.

[a] containing a is an element of X for an equivalence relation R in X is the subset of X containing all elements b related to a.

A function f : X → Y is defined to be , if the images of distinct elements of X under f are distinct, i.e., for every x1, x2 is an element of X, f(x1) = f(x2) implies x1 =x2.

A function f : X → Y is said to be , if every element of Y is the image of some element of X under f, i.e., for every y is an element of Y, there exists an element x in X such that f(x) = y.

A binary operation * on the set X is called , if a * b = b * a,for every a, b is an element of X.

A binary operation ∗ : A × A → A, an element e ∈ A, if it exists, is called ∗, if a ∗ e = a = e ∗ a, ∀ a ∈ A.

A function f : X → Y is if and only if f is one-one and onto.

RELATIONS AND FUNCTIONS

Gap-fill exercise