Design a synthesis for each of the following compounds using the given starting material:

a)

b)

c)

d)

(a)

The carbonyl group gives a nucleophilic addition reaction.In the given reaction nitrogen lone pair attacks the carbonyl group and we get the intermediate as shown below. In the further step, lone pair of nitrogen delocalizes and the double carbon attacks the ethyl bromide. Further, the acid hydrolysis of the following compound gives the resultant target molecule. Following is the mechanism of the reaction:

Reaction (a)

(b)

In the first step${}^{\text{-}}{\text{CH}}_{\text{2}}$attacks the carbonyl group and methoxy group is removed as a leaving group and we get the ring structure as shown below. Again, in the next step ethyl bromide attacks the carbonyl group followed by acid hydrolysis giving the resultant target molecule.

The mechanism is given below:

Reaction (b)

(c)

Acetaldehyde when reacting with the LDA then hydrogen of $\mathbf{-}{\mathbf{CH}}_3$is removed.In the next step the negatively charged carbon is attacked on the carbonyl compound. Further, oxidation of the aldehyde to carboxylic acid occurs using . The mechanism is as shown below:

Reaction (c)

(d)

In the first step, the methoxide ion abstracts the hydrogen of${\text{-CH}}_{\text{2}}$. Then the negatively charge carbon attacks further so that the rearrangement takes place followed by acid hydrolysis to give the target product.

The mechanism is shown below:

Reaction (d)