Relations and Functions Quiz

Let A and B be two sets. Then a relation R from set A to set B is a subset of A × B.

A relation R on a set A is said to be an empty relation iff R = ∅.

A relation R on a set A is said to be a universal relation iff R = A × A.

A relation R on A is reflexive if for all a ∈ A, a R a.

A relation R on A is symmetric if for all a, b ∈ A, a R b implies b R a.

A relation R on A is transitive if for all a, b, c ∈ A, a R b and b R c implies a R c.

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

Let R be an equivalence relation on a set A and let a ∈ A. Then, we define the equivalence class of a as [a] = {b ∈ A | b R a}.

Let A and B be two non-empty sets. Then a function ‘f’ from set A to set B is a rule which associates elements of set A to elements of set B such that: (a) All elements of set A are associated to elements in set B. (b) An element of set A is associated to a unique element in set B.

A curve in a plane represents the graph of a real function if and only if no vertical line intersects it more than once.