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.

e) is the correct one

Step-by-step explanation:

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.

2nd one in the first row is correct