Functional-Dependencies

Relational Schema:

Farmer(FID, FName, ContactNo, Address, Age, Income);
Crops(CName, Climate, Soil, Fertiliser);
Buyers(BID, BName, Age, ContactNo, Address, Annual_Inc, CompanyName);
Schemes(SchID, SName, Type, Eligibility, IssuedBy);
Quality(qfactor);
Farm_details(FID, CName, QFactor, CostPrice, Availability, SellingPrice, Sq.Area, District);
Transaction Details(FID, CName, QF, BID, DateofPurchase, Rate, QtySold);
Farmer-Scheme (FID, SchID, StartDate, EndDate) ;

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Canonical form of FDs:

FID -> { FName, ContactNo, Address, Age, Income }
Since the determinant in every FD is a SuperKey of the Farmer relation, it is in BCNF.

CName -> {Soil, Climate, Fertilizer}
Since the determinant in every FD is a SuperKey of the Crops relation, it is in BCNF.

BID -> { BName, Annual_Inc, ContactNo, Address, Age, CompanyName }
Since the determinant in every FD is a SuperKey of the Buyer Details relation, it is in BCNF.

SchID -> { SName, Type, Eligibility, IssuedBy}
Since the determinant in every FD is a SuperKey of the Schemes relation, it is in BCNF.

{FID, CName, QFactor} -> {Sq.Area, Availability, SellingPrice, CostPrice, District}
Since the determinant in every FD is a SuperKey of the Farm Details relation, it is in BCNF.

{FID, CName, QF, BID, DateOfPurchase} -> { QtySold, Rate }
Since the determinant in every FD is a SuperKey of the Transaction Details relation, it is in BCNF.

{ FID, SchID } -> {StartDate, EndDate}
Since the determinant in every FD is a SuperKey of the Farmer-Scheme relation, it is in BCNF.

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Minimal set of FDs:

FID -> FName
FID -> ContactNo
FID -> Address
FID -> Age
FID -> Income
CName -> Soil
CName -> Climate
CName -> Fertilizer
BID -> BName
BID -> Income
BID -> ContactNo
BID -> Address
BID -> Age
BID -> CompanyName
SchID -> SName
SchID -> Type
SchID -> Eligibility
SchID -> IssuedBy
{FID, CName, QFactor} -> Sq.Area
{FID, CName, QFactor} ->  Availability
{FID, CName, QFactor} -> SellingPrice
{FID, CName, QFactor} -> CostPrice
{FID, CName, QFactor} -> District
{FID, CName, QF, BID, DateOfPurchase} -> QtySold
{FID, CName, QF, BID, DateOfPurchase} -> Rate
{ FID, SchID } -> StartDate
{ FID, SchID } -> EndDate

All of the above relations are clearly in BCNF form.