Please fill in the blanks for the definitions specified below.

1. , , ,

............ , ............ , and .................. are some of the (non) commercial Database Management Systems. - 3 points.

2. Relational Data Model is based on the ................... theory in Math. -2 points.
3. Consider two relations called R₁ and R₂. The number of tuples in R₁ and R₂ are t₁ and t₂ respectively. The number of attributes of R₁ and R₂, on the other hand, are n₁ and n₂. (t₁, t₂, n₁, n₂ >= 1). Fill in the blanks with formulae containing t₁, t₂, n₁, n₂, functions, and constants. Each correct answer 2 points.

• If we apply RESTRICT operator to the relation R₁, the result will contain a minimum of and a maximum of tuples. The result relation will have a minimum of and a maximum of attributes.
• If we apply PROJECT operator to the relation R₂, the result will contain a minimum of and a maximum of tuples. The result relation will have a minimum of and a maximum of attributes.
• Assuming that R₁ and R₂ are union-compatible, If we UNION R₁ and R₂ relations, the result will contain a minimum of and a maximum of tuples. The result relation will have a minimum of and a maximum of attributes.
• f we q-JOIN R₁ and R₂ over an attribute ( or a set of attributes), the result will contain a minimum of and a maximum of tuples. The result relation will have a minimum of and a maximum of attributes.