Consider the following statements:
$(1)$ Bridgehead halides are inert towards both $S_{N^1}$ and $S_{N^2}$ reactions (until one of the ring size is an eight-membered ring).
$(2)$ The first step in both $S_{N^1}$ and $E_1$ reactions is the same.
$(3)$ $S_{N^2}$ reactions proceed with total retention of configuration.
$(4)$ $E_2$ eliminations are favored by the use of a solvent of low polarity and a high concentration of a strong base.
Which of the above statements are correct?

  • A
    $1, 2$ and $4$
  • B
    $1$ and $3$
  • C
    $2, 3$ and $4$
  • D
    $1, 2, 3$ and $4$

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