Question

A new computer has a model number, a part number, and a serial number. The model number is assigned by the manufacturer to identify the type of computer. The part number identifies one part of the smaller components that make up the computer. The serial number is unique to each computer produced and identifies it. Which relation is a function? (serial number, model number) (part number, serial number) (model number, part number) (model number, serial number)

Answer 1

Answer:

The relation which is a function as well is:

(serial number, model number)

Step-by-step explanation:

It is given that:

• The model number is assigned by the manufacturer to identify the type of computer.

• The part number identifies one part of the smaller components that make up the computer.

• The serial number is unique to each computer produced and identifies it.

Now we are asked to find which relation is a function.

We know that a function is a relation such that it maps each element of one set to a single element of the other set.

In other words the image of an element is unique.

( i.e. there could not exist two image of an element whereas there could exist two elements such that both have the same image)

1)

(serial number,model number)

As corresponding two one serial number we will have a single model number.

Since serial number is unique.

so, each serial number will have a single model number.

Hence, the relation is a function.

2)

(part number, serial number)

As each part is used in different computers.

and hence, each part number can be mapped to mre than one serial number.

Hence, the relation is not a function.

3)

(model number,part number)

Since, the number of parts used to develop a computer are more.

As corresponding to each model number the number of parts are more than one, this means a model number will corresponds to so many part number and hence is not unique.

Hence, option 3) is not a function.

4)

(model number, serial number)

As corresponding to one model there may exist more than one computer system that has different serial number.

Hence, the image is not unique.

Hence, the relation is not a function.

Answer 2

(serial number, model number)

That's a function mapping each serial number to its model number.

 (part number, serial number)

That's not a function; the same part number is in computers with different serial numbers

 (model number, part number)

That one's a bit confusing.  Normally a given model would have more than one part number inside so this isn't a function.  But here the description says there's only one part number for each model, so that would be a function.

(model number, serial number)

Not a function, more than one serial number for a given model number.