MATH SOLVE

2 months ago

Q:
# 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

Accepted Solution

A:

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)=bf(b)=af(c)=cf(d)=db)f(a)=bf(b)=bf(c)=df(d)=cc)f(a)=df(b)=bf(c)=cf(d)=dStep-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)=bf(b)=af(c)=cf(d)=dAll 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.