Identify `(A), (B), ` and `(C)` in the following reaction.

Explanation

D.U. in (A)`=((2n_(C)+2)-n_(H))/(2)=((7xx2+2)-10)/(2)=3^(@)`
`D.U. ` in `B=((7xx2+2)-14)/(2)=1^(@)`
`(A)` does not react with `P-2` or Brown catalyst `(Ni_(2)b)` that reduced `(C-=C)` to `(C-=C)`.
Therefore, `(A)` does not containe `(C-=C)` bond.
Since `(B)` has `1 D.U.`, it must be a ring (because after hydrogenation of `(A)` no double bond will be left).
Therefore, `(A)` has one ring and two `(C-=C)` bonds, hence, `(A)` is a diene.
`{:("Total number of C atom in" (A)=7),("Total number of C atoms in" (C)=6):}]` one C at om is lost as `CO_(2)`
Possible structures of `(A)` are as follows `:`
i.
`ii.` Other two possiblities of the combination are as follows `:`
a. `overset(1)(C)OOH` group combines with `overset(4)C=0` group and `overset(7)(C)O_(2)` combination with `overset(6)(C)OOH`.

b. `overset(6)(C)OOH` group with `overset (4)(C)=O` group and `CO_(2)` is in combination with `overset(1)(C)OOH`.

`III` structure is not possible , since on hydrogenation `(A)` gives `(B),(C_(7)H_(14))`, i.e., it absorbs `2 mol` of `H_(2)`, whereas `III` will absorb `3 mil` of `H_(2)`.
Moreover, `III` is unlikely because of highly strained ring.
Two possible structures are as follows `:`