Archangel Macsika
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.
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(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