a. Draw the end lobes of molecular orbitals of conjugated π-bonds in the following to show whether the HOMO is symmetric or antisymmetric.
i. A polyene with even numbers of π-bonds.ii. A polyene with odd numbers of π-bonds.
b. Do these MOs follow the Woodward–Hoffmann rules given below?
Woodward–Hoffmann rules:

• For an even number of π-bonds, an electrocyclic reaction occurs thermally with a conrotatory ring closure and photochemically with disrotatory ring closure.
• For an odd number of π-bonds electrocyclic reaction thermally with a disrotatory ring closure and photochemically with conrotatory ring closure.