What is the difference between a relation and a function?

a.A function is a set of ordered pairs; a relation is a special kind of function in which no two ordered pairs have the same second coordinate.

b.A function is a set of ordered pairs; a relation is a special kind of function in which no two ordered pairs have the same first coordinate.

c.A relation is a set of ordered pairs in which no two ordered pairs have the same first coordinate; a function is a set of ordered in which no two ordered pairs have the same second coordinate.

d.A relation is a set of ordered pairs; a function is a special kind of relation in which no two ordered pairs have the same second coordinate.

e.A relation is a set of ordered pairs; a function is a special kind of relation in which no two ordered pairs have the same first coordinate.

A function is a set of order pairs in which the first coordinate appears only once, it is a special kind of relation. Option e) is the one matching the definition.

a) A set of order pairs is not a function, but a relation. A special kind of function which no to ordered pairs have the same second coordinate is an injective function.

b) A special kind of function in which no two ordered pairs have the same first coordinate is just a function

c) A set of ordered pairs in which no two ordered pairs have the same first coordinate is a function, not a relation. The definition of function is wrong, but a set of order pairs in which no two ordered pairs have the same first coordinate, and also no two ordered pairs have the same second coosrinate is a injective funciton.

d) The definition for relation is correct, but in the definition of funciton it is not the second coordinate, but the first one.