In MYSQL database, if a table, Alpha has degree 5 and cardinality 3, and another table, Beta has degree 3 and cardinality 5, what will be the degree and cardinality of the Cartesian product of Alpha and Beta?
a. 5,3
b. 8,15
c. 3,5
d. 15,8
Answer
Answer by student:
b. 8,15
Detailed answer by teachoo:
To answer this question, we need to know the definitions of degree, cardinality, and Cartesian product of tables in MYSQL database.
- The degree of a table is the number of columns or attributes it has. For example, if a table has 5 columns, its degree is 5.
- The cardinality of a table is the number of rows or tuples it has. For example, if a table has 3 rows, its cardinality is 3.
- The Cartesian product of two tables is a table that contains all possible combinations of rows from the two tables. The degree of the Cartesian product is the sum of the degrees of the two tables. The cardinality of the Cartesian product is the product of the cardinalities of the two tables.
Let’s go through each of the options and see why they are correct or incorrect:
- a. 5,3: This is incorrect because it is the same as the degree and cardinality of Alpha. The Cartesian product should have a higher degree and cardinality than either of the original tables.
- b. 8,15: This is correct because it follows the formula for the degree and cardinality of the Cartesian product.
Degree = 5 + 3 = 8 and Cardinality = 3 * 5 = 15.
- c. 3,5: This is incorrect because it is the same as the degree and cardinality of Beta. The Cartesian product should have a higher degree and cardinality than either of the original tables.
- d. 15,8: This is incorrect because it swaps the values for the degree and cardinality. The degree should be the sum of the degrees, not the product. The cardinality should be the product of the cardinalities, not the sum.
So, the correct answer is b. 8,15.