Answer:
Only function (a) is one-to-one.
Step-by-step explanation:
If every element of the range of the function corresponds to exactly one element of the domain, then the function is called one-to-one.
The elements of a function are
A = {a,b,c,d}
We need to check whether [tex]f\rightarrow A\times A[/tex] is one to one or not.
(a)
f (a) = b, f (b) = a, f (c) = c, f (d) = d
Here, for each value of x, there exist exactly one value of y.
Therefore, this function is one-to-one.
(b)
f (a) = b, f (b) = b, f (c) = d, f (d) = c
Here, the value of function is b for x=a and x=b. For two domains the functions has same range.
Therefore, this function is not one-to-one.
(c)
f (a) = d, f (b) = b, f (c) = c, f (d) = d
Here, the value of function is d for x=a and x=d. For two domains the functions has same range.
Therefore, this function is not one-to-one.
