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A pericyclic reaction (rearrangement) involving the conversion of a pi bond to a sigma bond or vice-versa is referred to as an electrocyclic reaction.

The reaction between two pi bonds of two molecules resulting in a cyclic structure is termed a cycloaddition reaction.

The sigmatropic reaction involves the cleavage of a sigma $\left(\mathrm{σ}\right)$ bond followed by the rearrangement of a pi $\left(\mathrm{π}\right)$ bond and the formation of a sigma bond.

a.

Reaction a

The reaction involves the conversion of a sigma bond to a pi bond.

Therefore, it is an electrocyclic reaction.

b.

Reaction b

The reaction involves the conversion of two pi bonds to two sigma bonds, resulting in a cyclic structure.

Therefore, the given reaction is a cycloaddition reaction.

c.

Reaction c

Here, a pi bond gets converted into a sigma bond. Therefore, the given reaction is electrocyclic.

d.

Reaction d

The reaction involves the cleavage of a sigma bond and the migration of a pi bond.

Therefore, it is a sigmatropic rearrangement reaction.