An incorrect statement with respect to $S_N1$ and $S_N2$ mechanisms for alkyl halides is

Question

A competing reaction for an $S_N2$ reaction is rearrangement.

A weak nucleophile and a protic solvent increase the rate or favour the $S_N1$ reaction.

A strong nucleophile in an aprotic solvent increases the rate or favours the $S_N2$ reaction.

$S_N1$ reactions can be catalysed by some Lewis acids.

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