In: Advanced Math
True or False. If true, quote a relevant theorem or reason, or give a proof. If false, give a counterexample or other justification.
There is a one-to-one and onto map between the open interval (0, 1) and the open interval (4, 8).
Here the given statement "There is a 1-1(one-one) and onto map between the open interval (0, 1) & the open interval (4, 8)." is
True
So for this We have map f: (0, 1) -----------> (4, 8)
such that f(x) = 4x + 4 ; x is in (0, 1)
so this map is one to one map and onto also.For this
Here note that values of f at x=0 and x=1 are not in (4, 8).