Examine the three quantities x = E/B , y = 1/μ_0 _0 and z =...

The quantity $x = \dfrac{E}{B}$ represents the ratio of the electric field to the magnetic field. From the Lorentz force equations $F = qE$ and $F = qvB$, we get $v = \dfrac{E}{B}$. Thus, the dimensional formula of $x$ is $[L T^{-1}]$.

The quantity $y = \sqrt{\dfrac{1}{\mu_0 \varepsilon_0}}$ represents the speed of light in a vacuum, $c$. Thus, the dimensional formula of $y$ is $[L T^{-1}]$.

The quantity $z = \dfrac{l}{CR}$ involves length $l$, capacitance $C$, and resistance $R$. The product $CR$ represents the time constant of an RC circuit, which has the dimension of time $[T]$. Since $l$ has the dimension of length $[L]$, the dimensional formula of $z$ is $\dfrac{[L]}{[T]} = [L T^{-1}]$.

Since $x$, $y$, and $z$ all have the same dimensional formula $[L T^{-1}]$, any pair chosen from them will possess identical dimensions. Therefore, $z$ and $x$, $x$ and $y$, and $y$ and $z$ all possess identical dimensions.