Logical expressions
Boolean1°. Given integer A, verify the following proposition: "The number A is positive".
Boolean2°. Given integer A, verify the following proposition: "The number A is odd".
Boolean3°. Given integer A, verify the following proposition: "The number A is even".
Boolean4°. Given two integers A and B, verify the following proposition: "The inequalities A > 2 and B ≤ 3 both are fulfilled".
Boolean5°. Given two integers A and B, verify the following proposition: "The inequality A ≥ 0 is fulfilled or the inequality B < −2 is fulfilled".
Boolean6°. Given three integers A, B, C, verify the following proposition: "The double inequality A < B < C is fulfilled".
Boolean7°. Given three integers A, B, C, verify the following proposition: "The number B is between A and C".
Boolean8°. Given two integers A and B, verify the following proposition: "Each of the numbers A and B is odd".
Boolean9°. Given two integers A and B, verify the following proposition: "At least one of the numbers A and B is odd".
Boolean10°. Given two integers A and B, verify the following proposition: "Exactly one of the numbers A and B is odd".
Boolean11°. Given two integers A and B, verify the following proposition: "The numbers A and B have equal parity".
Boolean12°. Given three integers A, B, C, verify the following proposition: "Each of the numbers A, B, C is positive".
Boolean13°. Given three integers A, B, C, verify the following proposition: "At least one of the numbers A, B, C is positive".
Boolean14°. Given three integers A, B, C, verify the following proposition: "Exactly one of the numbers A, B, C is positive".
Boolean15°. Given three integers A, B, C, verify the following proposition: "Exactly two of the numbers A, B, C are positive".
Boolean16°. Given a positive integer, verify the following proposition: "The integer is a twodigit even number".
Boolean17°. Given a positive integer, verify the following proposition: "The integer is a threedigit odd number".
Boolean18°. Verify the following proposition: "Among three given integers there is at least one pair of equal ones".
Boolean19°. Verify the following proposition: "Among three given integers there is at least one pair of opposite ones".
Boolean20°. Given a threedigit integer, verify the following proposition: "All digits of the number are different".
Boolean21°. Given a threedigit integer, verify the following proposition: "All digits of the number are in ascending order".
Boolean22°. Given a threedigit integer, verify the following proposition: "All digits of the number are in ascending or descending order".
Boolean23°. Given a fourdigit integer, verify the following proposition: "The number is read equally both from left to right and from right to left".
Boolean24°. Three real numbers A, B, C are given (A is not equal to 0). By means of a discriminant D = B^{2} − 4·A·C, verify the following proposition: "The quadratic equation A·x^{2} + B·x + C = 0 has real roots".
Boolean25°. Given two real numbers x, y, verify the following proposition: "The point with coordinates (x, y) is in the second coordinate quarter".
Boolean26°. Given two real numbers x, y, verify the following proposition: "The point with coordinates (x, y) is in the fourth coordinate quarter".
Boolean27°. Given two real numbers x, y, verify the following proposition: "The point with coordinates (x, y) is in the second or third coordinate quarter".
Boolean28°. Given two real numbers x, y, verify the following proposition: "The point with coordinates (x, y) is in the first or third coordinate quarter".
Boolean29°. Given real numbers x, y, x_{1}, y_{1}, x_{2}, y_{2}, verify the following proposition: "The point (x, y) is inside of the rectangle whose left top vertex is (x_{1}, y_{1}), right bottom vertex is (x_{2}, y_{2}), and sides are parallel to coordinate axes".
Boolean30°. Given three integers a, b, c that are the sides of a triangle, verify the following proposition: "The triangle with sides a, b, c is equilateral".
Boolean31°. Given three integers a, b, c that are the sides of a triangle, verify the following proposition: "The triangle with sides a, b, c is isosceles".
Boolean32°. Given three integers a, b, c that are the sides of a triangle, verify the following proposition: "The triangle with sides a, b, c is a right triangle".
Boolean33°. Given three integers a, b, c, verify the following proposition: "A triangle with the sides a, b, c exists".
Boolean34°. Given coordinates x, y of a chessboard square (as integers in the range 1 to 8), verify the following proposition: "The chessboard square (x, y) is white". Note that the left bottom square (1, 1) is black.
Boolean35°. Given coordinates x_{1}, y_{1}, x_{2}, y_{2} of two chessboard squares (as integers in the range 1 to 8), verify the following proposition: "Both of the given chessboard squares have the same color".
Boolean36°. Given coordinates x_{1}, y_{1}, x_{2}, y_{2} of two chessboard squares (as integers in the range 1 to 8), verify the following proposition: "A rook can move from one square to another during one turn".
Boolean37°. Given coordinates x_{1}, y_{1}, x_{2}, y_{2} of two chessboard squares (as integers in the range 1 to 8), verify the following proposition: "A king can move from one square to another during one turn".
Boolean38°. Given coordinates x_{1}, y_{1}, x_{2}, y_{2} of two chessboard squares (as integers in the range 1 to 8), verify the following proposition: "A bishop can move from one square to another during one turn".
Boolean39°. Given coordinates x_{1}, y_{1}, x_{2}, y_{2} of two chessboard squares (as integers in the range 1 to 8), verify the following proposition: "A queen can move from one square to another during one turn".
Boolean40°. Given coordinates x_{1}, y_{1}, x_{2}, y_{2} of two chessboard squares (as integers in the range 1 to 8), verify the following proposition: "A knight can move from one square to another during one turn".
