Draw the product of each of the following sigmatropic rearrangements:

Sigmatropic reactions fall under the category of pericyclic reactions. In the transition state of a sigmatropic rearrangement, the group that drifts is partially connected to the migratory origin and the migration terminus.

a. The given compound undergoes a [3,3] sigmatropic rearrangement to form 6-(but-3-en-2-yl) cyclohexa-2,4-dienone. It further undergoes tautomerization to form 2-(but-3-en-2-yl)phenol. The reaction is shown below.

Reaction (a)

b. The given compound undergoes a [3,3] sigmatropic rearrangement to form (E)-6-(but-2-en-1-yl)cyclohexa-2,4-dienone. It further undergoes tautomerization to form (E)-2-(but-2-en-1-yl)phenol.

The reaction is shown below.

Reaction (b)

c. The given compound undergoes a [5,5] sigmatropic rearrangement to form (E)-4-methyl-4-(penta-2,4-dien-1-yl)cyclohexa-2,5-dienone. It further undergoes tautomerization to form (E)-4-(penta-2,4-dien-1-yl)phenol.

The reaction is shown below.

Reaction (c)

d. The given compound undergoes a [5,5] sigmatropic rearrangement to form (E)-4-(penta-2,4-dien-1-yl)cyclohexa-2,5-dienone. It further undergoes tautomerization to form 4-((2E,4E)-hexa-2,4-dien-1-yl)phenol.

The reaction is shown below.

Reaction (d)