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IGNOU BCA AND MCA MCS-013 Solved Assignment 2017-18

MCS-013 Discrete Mathematics

Question 1 (a) Explain different logical connectives with the help of examples.
(b) Make truth table for followings:
i) p→(q ~ r) (~p ~r)   
ii) p→(r ~ q)   (~p ~q) 
(d) Explain logical equivalence with the help of example.

Question 2
(a) Write down suitable mathematical statement that can be represented by the following symbolic properties.
i) ( x) ( y) ( z) P   
ii) ( x) ( y) ( z) P   
(c) What is indirect method of proof? Example with example.
(d) What is relation? Explain equivalence relation with the help of an example.

Question 3
(b) Find dual of Boolean Expression for Q, in the figure given below.
Figure 1: Logic Circuit
(c) Explain De Morgan’s laws in relation to Boolean Algebra.
(d) What is principle of mathematical induction? Explain with the help of an example.

Question 4
(a) How many different committees can be formed of 12 professionals, each containing at least 2 Professors, at least 3 Lecturers and 3 Administrative Officers from a set of 5 Professors, 8 Lectures and 5 Administrative Officers.
(c) What is set? Explain the basic properties of sets.

Question 5
(a) How many words can be formed using letter of UNIVERSITY using each letter at most once?
i) If each letter must be used,
ii) If some or all the letters may be omitted.
(c) Explain whether (p q) (q r) is a tautology or not.   
(d) Explain addition theorem in probability.
(e) Prove that the inverse of one-one onto mapping is unique.

Question 6 (a) How many ways are there to distribute 15 district objects into 5 distinct boxes with:
i) At least three empty box.
ii) No empty box.
(b) Explain principle of multiplication with an example.
(c) Set A,B and C are: A = {1, 2, 3,5, 8, 11 12,13}, B = { 1,2, 3 ,4, 5,6 } and C={ 7,8,12, 13}. Find A B C , A B C, A B C and (B~C)      
(d) In a class of 40 students; 30 have taken science; 20 have taken mathematics and 8 has neither taken mathematic nor science. Find how many students have taken:
i) both subjects.
ii) exactly one subject

Question 7
(a) What is power set? Write power set of set A={1,2,5,6,7,9}.
(b) Draw truth table for and explain whether it is a tautology or not.
(c) What is a function? Explain domain and range in context of function, with the help of example.
(d) State and prove the Pigeonhole principle.

Question 8
(a) Find inverse of the following functions
(b) Explain circular permutation with the help of an example.
(c) Give geometric representation for followings:
i) { 3} x R
ii) {1, 2) x ( 2, 3)
(d) Show whether √15 is rational or irrational.



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