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Programming Taskbook |
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1100 training tasks on programming |
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© M. E. Abramyan (Southern Federal University, Shenzhen MSU-BIT University), 1998–2024 |
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Logical expressionsAll tasks in this group require determining the proposition as True or False. All numbers with fixed amount of digits (for example, two-digit number, three-digit number and so on) are assumed to be positive integers. 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 two-digit even number". Boolean17°. Given a positive integer, verify the following proposition: "The integer is a three-digit 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 three-digit integer, verify the following proposition: "All digits of the number are different". Boolean21°. Given a three-digit integer, verify the following proposition: "All digits of the number are in ascending order". Boolean22°. Given a three-digit integer, verify the following proposition: "All digits of the number are in ascending or descending order". Boolean23°. Given a four-digit 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 = B2 − 4·A·C, verify the following proposition: "The quadratic equation A·x2 + B·x + C = 0 has real roots". Boolean25°. Given two nonzero real numbers x, y, verify the following proposition: "The point with coordinates (x, y) is in the second coordinate quarter". Boolean26°. Given two nonzero real numbers x, y, verify the following proposition: "The point with coordinates (x, y) is in the fourth coordinate quarter". Boolean27°. Given two nonzero 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 nonzero 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, x1, y1, x2, y2, verify the following proposition: "The point (x, y) is inside of the rectangle whose left top vertex is (x1, y1), right bottom vertex is (x2, y2), 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 x1, y1, x2, y2 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 x1, y1, x2, y2 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 x1, y1, x2, y2 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 x1, y1, x2, y2 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 x1, y1, x2, y2 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 x1, y1, x2, y2 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".
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