Question

Which of the relations below is a function?

A) {(red, sign) (yellow, sign) (red, light) (green, light)}
B) {(red, apple) (purple, grape) (yellow, banana) (green, pear)}
C) {(blue, bird) (red, car) (yellow, bus) (yellow, taxi)}

Answer 1

Out of the three relations given, only Relation B is a function because each input is associated with exactly one output, which is a requirement for a function.

Step-by-step explanation:

To determine which of the relations is a function, we need to check each pair in the sets. A function is a relation where each input has a unique output.

• Relation A: {(red, sign), (yellow, sign), (red, light), (green, light)} has the input 'red' associated with two different outputs ('sign' and 'light'), so this is not a function.
• Relation B: {(red, apple), (purple, grape), (yellow, banana), (green, pear)} has each input color associated with exactly one fruit, which makes this a function.
• Relation C: {(blue, bird), (red, car), (yellow, bus), (yellow, taxi)} has the input 'yellow' associated with two different outputs ('bus' and 'taxi'), which means it is not a function.

Hence, the only relation that is a function is Relation B.