Course X Student;
where 'Course' and 'Student' are two relations and X is an operation.
Relational Algebra Operations Explained
Relational algebra is a procedural query language used in relational database systems. It defines a set of operations that can be applied to relations (tables) to retrieve or manipulate data. These operations form the basis for many database query languages, including SQL.
Understanding the Cartesian Product Operation
The question presents a notation commonly found in relational algebra: 'Course X Student', where 'Course' and 'Student' represent two database relations, and 'X' denotes a specific operation. We need to identify this operation.
The Cartesian product is one of the fundamental operations in relational algebra. It combines every tuple (row) from the first relation with every tuple from the second relation. The symbol typically used for the Cartesian product is the multiplication sign, often written as $\times$. In the given notation, 'X' serves the same purpose as $\times$.
The Cartesian product of two relations, R and S, denoted as $R \times S$, generates a new relation that contains all possible combinations of rows from R and S. If relation R has $n$ rows and relation S has $m$ rows, the resulting relation $R \times S$ will have $n \times m$ rows.
Applying this to the question, 'Course X Student' signifies the Cartesian product between the 'Course' relation and the 'Student' relation. This operation would produce a result set where each course is paired with every student.
Analyzing Other Relational Algebra Operations
To confirm why 'Course X Student' specifically points to the Cartesian product, let's briefly consider the other common relational algebra operations:
- Union ($\cup$): Combines rows from two relations that have compatible schemas, eliminating duplicate rows.
- Set Difference ($-$ or $\setminus$): Returns rows that are present in the first relation but not in the second.
- Intersection ($\cap$): Returns rows that are common to both relations.
Since the notation uses 'X', which is the conventional symbol for the Cartesian product, this operation is the one being represented.
Important Questions from Miscellaneous
A stone is thrown horizontally from the top of a 20 m high building with a speed of 12 m/s. It hits the ground at a distance R from the building. Taking g = 10 m/s2 and neglecting air resistance will give :
A sphere of volume V is made of a material with lower density than water. While on Earth, it floats on water with its volume f1V (f1 < 1) submerged. On the other hand, on a spaceship accelerating with acceleration a < g (g is the acceleration due to gravity on Earth) in outer space, its submerged volume in water is f2V. Then:
A railway wagon (open at the top) of mass M1 is moving with speed v1 along a straight track. As a result of rain, after some time it gets partially filled with water so that the mass of the wagon becomes M2 and speed becomes v2. Taking the rain to be falling vertically and the water stationery inside the wagon, the relation between the two speeds v1 and v2 is :
Consider the following statements:
1. Distance between the longitudes becomes zero on North Pole and South Pole.
2. Distance between the longitudes is maximum on the Equator.
3. Number of longitudes is more than number of latitudes.
Which of the statements given above is/are correct?
One block of 2⋅0 kg mass is placed on top of another block of 3⋅0 kg mass. The coefficient of static friction between the two blocks is 0⋅2. The bottom block is pulled with a horizontal force F such that both the blocks move together without slipping. Taking acceleration due to gravity as 10 m/s2, the maximum value of the frictional force is :
