which of the following metric spaces are complete?

Which of the following metric spaces are complete?

  1. $X_1=(0,1), d(x,y)=|\tan x-\tan y|$

  2. $X_2=[0,1], d(x,y)=\frac{|x-y|}{1+|x-y|}$

  3. $X_3=\mathbb{Q}, d(x,y)=1\forall x\neq y$

  4. $X_4=\mathbb{R}, d(x,y)=|e^x-e^y|$

$2$ is complete as closed subset of a complete metric space is complete and the metric is also equivalent to our usual metric.

$3$ is also complete as every Cauchy sequence is constant ultimately hence convergent.

$4$ is not complete I am sure but not able to find out a counter example, not sure about 1.thank you for help.

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