Determine whether each of these functions from {a, b, c, d} to itself is one-to-one. a) f (a) = b, f (b) = a, f (c) = c, f (d) = d. b) f (a) = b, f (b) = b, f (c) = d, f (d) = c. c) f (a) = d, f (b) = b, f (c) = c, f (d) = d.

The first one is one-to-one.

The second one is not one-to-one.

Third one is not one-to-one.

The problem:

Are the following one-to-one from {a, b, c, d} to {a, b, c, d}:

a)

f (a) = b

f (b) = a

f (c) = c

f (d) = d

b)

f (a) = b

f (b) = b

f (c) = d

f (d) = c

c)

f (a) = d

f (b) = b

f (c) = c

f (d) = d

Step-by-step explanation:

One-to-one means that a y cannot be hit more than once, but all the y's from the range must be hit.

So the first one is one-to-one because:

f (a) = b

f (b) = a

f (c) = c

f (d) = d

All the elements that got hit are in {a, b, c, d} and all of them were hit.

The second one is not one-to-one.

The reason is because f (a) and f (b) both are b.

Third one is not one-to-one.

The reason is because f (a) and f (d) are both d.