Question

In: Advanced Math

True or False. If true, quote a relevant theorem or reason, or give a proof. If...

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).

Solutions

Expert Solution

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).

Colby Messinger answered 4 months ago
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