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
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Let us determine whether the function from to itself is one-to-one.
a)
Taking into account that preimage of each point is singleton:
we conclude that implies for any
and hence the function is one-to-one.