Question

Select either relation (if the set is a relation but not a function), function (if the set is both a relation and a function), or neither (if the set is not a relation).
A = {(1, 2) (2, 2) (3, 2) (4, 2)}

relation
function
neither

Answer 1

Answer:  The correct options are

(A) relation

(B) function.

Step-by-step explanation:  We are given to check whether the following set is a relation or a relation and a function or neither :

A = {(1, 2) (2, 2) (3, 2) (4, 2)} .

Let us consider the following two sets :

U = {1, 2, 3, 4}  and  V = {2}.

Then, we see that the Cartesian Product of U and V is given by

U × V = {(1, 2) (2, 2) (3, 2) (4, 2)}.

Since a relation is a subset of Cartesian product, so the given set A is a relation.

Also, we know that a relation is a function if every first element is associated with one second element.

Since the relation A satisfies this condition, so the relation A is a function.

Thus, the given set A is both a relation and a function.

Option (A) and (B) are correct.