-Given: 
Prove: 
Provide the missing reasons for this proof:
S1. 
R1.
S2. 
R2.
S3. 
R3.
S4. 
R4.
S5. 
R5.
Definitions:
Expensive Advertisement
High-cost marketing activities aimed at promoting products, services, or brands to a wide audience.
Product-variety Externality
An economic condition where the diversity of products benefits consumers more than what is accounted for by the producers, leading to positive external effects in a market.
Business-stealing Externality
A business-stealing externality occurs when the entry of new businesses reduces the demand for existing businesses, potentially lowering profits without necessarily benefiting consumers.
Positive Externality
An advantage received by individuals without their active choice, commonly linked to communal goods or services.
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