Show that the following pairs of sets have the same cardinality. 
(a) Integers divisible by 3, and the even positive integers.
(b) $\Bbb {R}$, and the interval $(0,\infty)$.
(c) The interval $[0, 2)$, and the set [5,6)∪[7,8).
(d) The intervals $(-\infty, -1)$ and $(-1, 0)$.

I know that cardinality means that there is a bijection between the two sets, and that means there is a surjection and injection. For the first one I think you can simply make a function that is a bijection and prove that it is an injection and surjection. I am not sure how to do the last three.
Sorry for the poor formatting in advance and if you need more information about the question I am more than happy to provide it.
Thank you.
 A: Hints:
(b) Map $x \in \mathbb{R}$ by $x \to e^x$
(c) Map $x \in [0, 2)$ by $x \to x + 5$ if $x \in [0,1)$ and $x \to x + 6$ if $x \in [1,2)$
(d) Map $x \in (-\infty,-1)$ by $x \to \frac{1}{x}$
Show that these are all bijections.
A: a) Let $A$ be a set of integers divisible by 3 and $C$ a set of positive even integers. You can take a composition of following functions. First $f:A\to \mathbb{Z}$ defined with $$n\longmapsto {n\over 3}$$
and then $g:\mathbb{Z}\to C$ defined by: 
$$
g(n)
\begin{cases}
= 4n+2     & \text{if } n\geq 0, \\
= 4|n| & \text{if } n < 0. \\
\end{cases}
$$
Then let $g\circ f$ will do the job.
A: (b) $\mathbb{R}$, and the interval (0,∞).
Consider $f : \mathbb{R}\rightarrow (0,\infty)$ defined by $f(x)=e^x.$
(c) The interval [0,2), and the set [5,6) or [7,8).
Consider $g: [0,2)\rightarrow [5,6)$ defined by $g(x)=5+\frac{x}{2}$ or $g'(x)=7+\frac{x}{2}$ if codomain is $[7,8)$.
(d) The intervals (−∞,−1) and (−1,0).
Consider $h: (-1,0)\rightarrow (-\infty,-1)$ defined by $h(x)=\tan(\frac{\pi}{2}x)-1.$
A: The bijections, reading left to right, can be chosen as:
(a) $|4x/3|+2[x\ge 0]$ (b) $x+\sqrt{1+x^2}$ (c) $x+5+\lfloor x\rfloor$ (d) $1/x$.
