QCM : Understanding Relations and Functions — 10 questions

Explication

Ordered pairs serve the main purpose of representing the connection between elements of two sets in a relation, explicitly showing the direction from the first component to the second, which is fundamental to the concept of relations as mappings.

Explication

The correct set is {(2, 5), (3, 7), (4, 9)} because in a function, each input (first element of the pair) must be unique and have only one output. The set with (2, 5) and (2, 6) includes the same input 2 with two different outputs, which violates the definition of a function. Therefore, the first set correctly represents a function, with each input mapped to exactly one output.

Explication

Ms. Rukhsana Jabeen is the author cited in the content for the work on Arrow Diagram Representation in 2026, making her the correct answer.

Explication

Ms. Rukhsana Jabeen is credited with defining the notation and fundamental concepts of functions in the context provided, making her the correct answer.

Explication

The formal concepts of domain and codomain were established during the late 19th century as part of the development of modern set theory and the formalization of functions, notably by mathematicians like Georg Cantor.

Explication

The range and the output set are essentially the same in the context of relations and functions, both representing the set of actual outputs produced by the relation or function.

Explication

The input variable causes or influences the output variable in a functional relationship, as the output depends on the input according to a specific rule, establishing a cause-effect relationship.

Explication

The key feature of a relation is that it involves a rule connecting pairs of elements from two sets with a directional property from the first set (domain) to the second set (codomain). This distinguishes relations from functions, which have additional constraints.

Explication

The correct answer is that a relation or mapping is a connection between elements of two sets with a rule that establishes a direction from the first set (domain) to the second set (codomain). This captures the essence of relations as connections with a rule and directionality, which is fundamental in the definition of relations and mappings.

Explication

A function is defined as a rule that assigns exactly one output to each input, ensuring a unique output for every input value, which distinguishes it from other types of relations.