Based on the information provided, we can create an Entity$-$Relationship $($ER$)$ diagram to represent the relationships between the entities mentioned in the proposal. Let's identify the entities, their attributes, and the relationships between them:

Inventory$/$Transaction Table:

Entity: Transaction

Attributes:

Transaction$\_$ID $($PK$)$

Product$\_$ID $($FK$)$

Quantity

Transaction$\_$Type

Transaction$\_$Date

Total Participation: Partial participation of Product$\_$ID $($assuming transactions without associated products are allowed$)$

Min, Max Constraint: $(1,1)$ for Transaction$\_$ID and $(0,1)$ for Product$\_$ID $($assuming transactions without associated products are allowed$)$

Transactions, Returns, Losses Table:

Entity: Transaction$\_$RRL $($for better distinction from the first table$)$

Attributes:

Transaction$\_$ID $($PK$)$

Product$\_$ID $($FK$)$

Quantity

Transaction$\_$Type

Transaction$\_$Date

Total Participation: Partial participation of Product$\_$ID $($assuming transactions without associated products are allowed$)$

Min, Max Constraint: $(1,1)$ for Transaction$\_$ID and $(0,1)$ for Product$\_$ID $($assuming transactions without associated products are allowed$)$

Login Table $-$ Method of Representing Users:

Entity: User

Attributes:

User$\_$ID $($PK$)$

Username

Password$\_$Hash

User$\_$Role

Total Participation: $(1,1)$ for User$\_$ID

Min, Max Constraint: N$/$A $($assuming every user must have a login record$)$

SKU Table:

Entity: SKU

Attributes:

Product$\_$ID $($PK$)$

Product$\_$Number

Product$\_$Name

Total Participation: $(1,1)$ for Product$\_$ID

Min, Max Constraint: N$/$A $($assuming every product must have an SKU record$)$

Now, let's represent the relationships:

Relationship between Transaction and SKU:

Name: Represents

Foreign Key: Product$\_$ID $($in Transaction$)$ references Product$\_$ID $($in SKU$)$

Type: Many$-$to$-$One $($Many transactions can be associated with one product$)$

Relationship between Transaction$\_$RRL and SKU:

Name: Represents

Foreign Key: Product$\_$ID $($in Transaction$\_$RRL$)$ references Product$\_$ID $($in SKU$)$

Type: Many$-$to$-$One $($Many transactions, returns, and losses can be associated with one product$)$

Relationship between User and Transaction:

Name: Performs

Foreign Key: User$\_$ID $($in Transaction$)$ references User$\_$ID $($in User$)$

Type: One$-$to$-$Many $($One user can perform many transactions$)$

This ER diagram should accurately represent the proposed database schema with the specified entities, their characteristics, and their connections.