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Symbolize the following by using qualifiers, predicates and logical connectives.


  1. All rational numbers are real numbers.
  2. some rational numbers are integers.
  3. some even numbers are multiplied of two four and five.
  4. some triangles are scalene.
  5. every integer is multiple of 10 if and only if it is a mulple of 5 and 2.

Write a java program that computes the area & perimeter of either a rectangle, a circle or a right-angled triangle. The program should display a menu that enables the user to select the type of figure whose area & perimeter he/she wants to compute. Depending on the users choice, the program should prompt for the dimensions and perform the computations. The output should be: - The type of figure, the dimensions, the area and the perimeter. (NB:The calculation should be for only one figure at any one time.)

using object oriented


Prove that every non-trivial sub group of cyclic group has finite index. Hence prove that (Q,+) is not cyclic.


A boy throws a ball of mass 0.293 - kg straight upward with an initial speed of 23m/s. When the ball returns to the boy, its speed is 18.24 m/s. How much work does air resistance do on the ball during its flight?


Differentiate between the various quality awards. 


3 a) Assume yourself to be an operations consultant, identify the various tools for establishing world-class standards in operations.

3.b. As an operations manager, comment on the role of the environment in world-class operations. 


Solution #1 is a 0.025 M solution of hypochlorous acid, HOCl (Ka = 3.0 × 10–8). Calculate each of the

following quantities for Solution #1.

(a) [H+] in Solution #1


why is beaker ,rather than a conical flask used ,when dissolving the solute.


Salt is often used to melt ice and snow on roads in the winter and the

temperature right now is -4.500ºC. How much NaCl (complete dissociation) would be

necessary to melt 1000kg of ice by bringing down the freezing temperature to -

4.500ºC?


when the solution has been made up ,why is it necessary to mix the contents of the flask thouroughly? what feature of the volumetric flask makes this particularly necessary


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