Predict the product of the following sigmatropic rearrangements. Be sure to rationalize the stereochemical outcome with a chair-like transition state.
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Sigmatropic rearrangements are a type of pericyclic reaction where a sigma bond adjacent to one or more pi systems migrates across the molecule. These reactions are characterized by the conservation of the total number of pi and sigma bonds and often involve a cyclic transition state. Understanding the specific type of sigmatropic shift, such as [1,5] or [3,3], is crucial for predicting the product.

A chair-like transition state is a conformation that resembles the chair form of cyclohexane, often adopted in pericyclic reactions to minimize steric strain and maximize orbital overlap. This conformation is particularly relevant in sigmatropic rearrangements as it helps rationalize the stereochemical outcome by providing a predictable spatial arrangement of substituents, leading to specific stereoisomers.

Stereochemistry in pericyclic reactions is governed by the conservation of orbital symmetry, as described by the Woodward-Hoffmann rules. These rules predict whether a reaction will proceed via a suprafacial or antarafacial pathway, influencing the stereochemical configuration of the product. In sigmatropic rearrangements, the stereochemical outcome is often determined by the geometry of the transition state, such as a chair-like conformation.