Define the five basic relational algebra operations. Define the Join, Intersection, and Division operations in terms of these five basic operations.

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Five basic operations are:
? Selection and Projection (Unary)
? Cartesian Product, Union, and Set Difference (Binary).
There is also the Join, Intersection, and Division operations:
? Can rewrite ?-Join in terms of the basic selection and Cartesian product operations:
R 3 F S = ?F (R ? S)
? Can express the intersection operation in terms of the set difference operation:
R ? S = R - (R - S)
? Can express the division operation in terms of the basic operations:
T 1 = ? C (R)
T 2 = ? C ( (S x T 1 ) - R)
T = T 1 - T 2

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Write a program that tests whether the examples of the math library function calls below actually produce the indicated results.

``` ex06_02.cpp #include using namespace std; int cube(int y); // function prototype int main() { int x{0}; for (x = 1; x <= 10; x++) { // loop 10 times cout << cube(x) << endl; // calculate cube of x and output results } } // definition of function cube int cube(int y) { return y * y * y; } ``` ``` // ex06_03.cpp // Testing the math library functions. #include #include #include using namespace std; int main() { cout << fixed << setprecision(1); cout << "sqrt(" << 9.0 << ") = " << sqrt(9.0); cout << "\nexp(" << 1.0 << ") = " << setprecision(6) << exp(1.0) << "\nexp(" << setprecision(1) << 2.0 << ") = " << setprecision(6) << exp(2.0); cout << "\nlog(" << 2.718282 << ") = " << setprecision(1) << log(2.718282) << "\nlog(" << setprecision(6) << 7.389056 << ") = " << setprecision(1) << log(7.389056); cout << "\nlog10(" << 10.0 << ") = " << log10(10.0) << "\nlog10(" << 100.0 << ") = " << log10(100.0) ; cout << "\nfabs(" << 5.1 << ") = " << fabs(5.1) << "\nfabs(" << 0.0 << ") = " << fabs(0.0) << "\nfabs(" << -8.76 << ") = " << fabs(-8.76); cout << "\nceil(" << 9.2 << ") = " << ceil(9.2) << "\nceil(" << -9.8 << ") = " << ceil(-9.8); cout << "\nfloor(" << 9.2 << ") = " << floor(9.2) << "\nfloor(" << -9.8 << ") = " << floor(-9.8); cout << "\npow(" << 2.0 << ", " << 7.0 << ") = " << pow(2.0, 7.0) << "\npow(" << 9.0 << ", " << 0.5 << ") = " << pow(9.0, 0.5); cout << setprecision(3) << "\nfmod("<< 2.6 << ", " << 1.2 << ") = " << fmod(2.6, 1.2) << setprecision(1); cout << "\nsin(" << 0.0 << ") = " << sin(0.0); cout << "\ncos(" << 0.0 << ") = " << cos(0.0); cout << "\ntan(" << 0.0 << ") = " << tan(0.0) << endl; } ```

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When an exception occurs in a method, you can use the method printStackTrace to determine the order in which the methods were called and where the exception was handled.

Answer the following statement true (T) or false (F)

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The reflow operation is one of the easiest in a B-tree.

Answer the following statement true (T) or false (F)

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