Consider the following statements :
(1) Bridge-head halides are inert towards both ${\mathrm{S}}_{{\mathrm{N}}^1}$ and ${\mathrm{S}}_{{\mathrm{N}}^2}$ reactions (till one of the ring size is eight member ring)
(2) The first step in both ${\mathrm{S}}_{{\mathrm{N}}^1}$ and E₁ reactions is the same
(3) ${\mathrm{S}}_{{\mathrm{N}}^2}$ reactions proceed with total retention of configuration
(4) E₂ eliminations are by the use of a solvent of low polarity and high concentration of a strong base.

Which of the above statements are correct?