Answer:
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
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.