Predict the nature of products formed by the catalytic hydrogenation of each of the following reactions.

$\left(\mathrm{b}\right)$ trans-Hex-$2$-ene

Predict the major product of the following reactions, including stereochemistry.

(a) Cyclohexene + peroxyacetic acid in water

Predict the major product of the following reaction including stereochemistry.

Methylenecyclohexane $+ {\mathrm{OsO}}_4, {\mathrm{NaHSO}}_3$

Predict the major product of the following reactions, including stereochemistry.

$\left(\mathrm{c}\right)$ cis$-2-$Pentene $+ {\mathrm{OsO}}_4/{\mathrm{H}}_2{\mathrm{O}}_2$

Predict the major product of the following reactions, including stereochemistry.

(d) cis$-2-$Pentene + peroxyacetic acid in water

Predict the major product of the following reactions, including stereochemistry.

$\left(\mathrm{e}\right)$ trans$-2-$Pentene $+ {\mathrm{OsO}}_4/{\mathrm{H}}_2{\mathrm{O}}_2$

Predict the major product of the reactions including stereochemistry.

trans$-2-$Pentene $+$ peroxyacetic acid in water

Propose a mechanism for the following reactions: