IGNOU Master of Computer Applications (MCA) :: Assignments

Course Code MCS-013
Course Title Discrete Mathematics
Assignment Number MCA(1)/013/ Assign /07
Maximum Marks 100
Weightage 25%
Last Date of Submission 15th April, 2007

There are eight questions in this assignment. Answer all questions. 20 Marks are for viva-voce. You may use illustrations and diagrams to enhance explanations. Please go through the guidelines regarding assignments given in the Programme Guide for the format of presentation.

Q1 : (4+2+4=10 Marks)
  1. Make truth table for the following:
    1. p→(~q ∨~r) ∧p ∧~q
    2. p→r ∨ ~q∧p ∨r
  2. What are conditional connectives? Give an example of biconditional statement.
  3. Write down suitable mathematical statement that can be represented by the following symbolic properties.
    1. (∃x) (∀y) P
    2. ∀(x) (∃y) (∀z) P
Q2: (6+4=10 Marks)
  1. Explain different methods of proof with the help of one example each.
  2. Show whether √17 is rational or irrational.
Q3: (5+5=10 Marks)
  1. What is logic circuit? Explain how Boolean algebra methods are used in logic circuit design.
  2. If p and q are statements, show whether the statement [(~p→ ~q) ∧ (q)] → (p∨q) is a tautology or not.
Q4: (4+4+2=10 Marks)
  1. Make logic circuit for the following Boolean expressions:
    1. (x'.y + z) + (x+z)'
    2. x'.y'+ y.z'+z'.x' + x' +y
  2. Find dual of Boolean expression for the output of the following logic circuit:
  3. Set A, B and C are:
    A = {1, 2, 3, 4, 9}, B = { 1,2 } and C { 2, 5,11 }find A∩B∪C and A∪B∩C
Q5: (4+4+2=10 Marks)
  1. Draw a Venn diagram to represent followings:
    1. (A B) ∪ (C~A)
    2. (A∪B) ∩ (B~C)
  2. Give geometric representation for following:
    1. {3} x R
    2. {1, 2) x ( 2, -3)
  3. Explain the use of counter example.
Q6: (4+6=10 Marks)
  1. What is inclusion-exclusion principle? Also explain one application of inclusion-exclusion principle.
  2. Find inverse of the following functions:
    1. f(x) =
    2. f(x) =
Q7: (4+4+2=10 Marks)
  1. How many 4 digit numbers are even? How many 4-digit numbers are composed of odd digits?
  2. How many different 15 persons committees can be formed each containing at least 8 women and at least one man from a set of 10 women and 12 men?
  3. Explain Bijective mapping with an example.
Q8: (4+4+2=10 Marks)
  1. What are Demorgan's Law? Also explain the use of Demorgan's law with example?
  2. How many ways are there to distribute 20-distinct object into 10 distinct boxes with
    1. At least three empty box.
    2. No empty box.
  3. Explain principle of multiplication with an example.

 
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