Answer to Question #140314 in Discrete Mathematics for Promise Omiponle

Question

Determine if each of the following functions from {a,b,c,d} to itself is one-to-one and/or onto.
Check ALL correct answers.
(a) f(a)=d,f(b)=a,f(c)=c,f(d)=b


A. onto.
B. neither one-to-one nor onto.
C. one-to-one.
f(a)=b,f(b)=a,f(c)=c,f(d)=d


A. one-to-one.
B. onto.
C. neither one-to-one nor onto.
f(a)=c,f(b)=d,f(c)=a


A. one-to-one.
B. onto.
C. neither one-to-one nor onto.

Answer 1

(a) Since a, b, c, d belong to the codomain of the function, it is onto. It is one-to-one because all points are transformed into different points. The answer is as follows: it is both one-to-one and onto ( A and C).

(b) Since a, b, c, d belong to the codomain of the function, it's onto. It is one-to-one because all points are transformed into different points. The answer is as follows: it is both one-to-one and onto (A and B).

(c) The element b is not included into the codomain of the function, so it is not onto. It is one-to-one because all points are transformed into different points. The answer is A. one-to-one