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MCS013 Important questions with solutions and Old/Previous
years questions papers with solutions (June 2014 to June 2019) 

Unit 
Topic 
1. 
Propositional Calculus 
2. 
Method of Proof 
3. 
Logic Circuits 
4. 
Set, Relations and Functions 
5. 
Combinatorics 
6. 
Counting Principle 
7. 
Partition and Distribution 
Old/Previous
Question Papers 

8. 
Old/Previous Question Papers with Solutions (June 2014 to june 2019) 
9. 
Guess Questions, upcoming exam import questions 

Notes1
1. (a) Write down the truth table of
p→q⋀∼r↔r⊕q.
Also explain whether it is a tautology or not.
(b) Show that √5 is irrational.
(c) Give the geometric representation of R x ⁽2⁾.
(d) Find the f inverse of the function
f : f(x) = x3 — 3.
(e) Present a direct proof of the statement : "Square of an odd integer is odd."
(f) How many permutations are there for the word 'UNIVERSITY" ?
2. (a) (i) Check whether (A U B) ⋂ C.AU (B ⋂ C) or not,using Venn Diagram.
(ii) Find the dual of A U (B U C).
(b) Prove that C (n, r) = C (n, n — r), for 0 ≤ r ≤ n,n∊ N.
3. (a) State and prove Addition Theorem of Probability.
(b) Show that in any group of 30 people, we can always find 5 people who were born on
the same day of the week.
(c) State Pigeonhole principle. Also give an example of its application.
4. (a) What is the probability that a number between 1 and 200 is divisible by neither 2, 3, 5 nor 7 ?
(b) In how many ways can 20 students be grouped into 3 groups ?
(c) In how many ways can r distinct objects be distributed into 6 different boxes with at least two boxes empty ?
5. (a) Give an example of a compound proposition that is neither a tautology nor a contradiction.
(b) Show that 2'1 > n3 for n > 10.
(c) Draw the logic circuit for the following boolean expression :
x.y + x. y' + x. y.
Notes2
1. (a) Let A = fa, b, c, d}, B = 11, 2, 3} and R = ((a, 2), (b, 1), (c, 2), (d, 1)1. Is R a function ? Why ?
(b) Under what conditions on sets A and B, AxB=B x A? Explain.
(c) How many bit strings of length 8 contain at least four 1s ?
(d) Show that the proposition p + q and  p v q are logically equivalent ?
(e) Use mathematical induction to show that n! > 2111 for n > 1. (0 A coin is tossed n times. What is the
probability of getting exactly r heads ?
(g) Prove that if x and y are rational numbers, then x + y is rational.
2. (a) Find f 1, where f is defined by fix) = x3  3 where x ∊ R.
(b) Let the set A = {1, 2, 3, 4, 5, 61 and R is defined as R = {(i, j) I I i  ji = 2}. Is IV transitive ? Is 'R' reflexive ? Is 'R'symmetric ?
3. (a) What are the inverse, converse and contra positive of the implication "If today is holiday then I will go for a movie." ?
(b) Draw the logic circuit for Y = AB'C + ABC' + AB'C'
(c) In how many ways can a prize winner choose three books from a list of 10 bestsellers, if repeats are allowed ?
4. (a) What is understood by the logical quantifiers ? How would you represent the following propositions and their negations using logical quantifiers :
(i) There is a lawyer who never tells lies.
(ii) All politicians are not honest.
(b) Show that (∼p∧n(∼q∧r))v(q∧r)v(p∧r)⇔r
(c) Define Modus Tollens.
5. (a) If R is the set of all real numbers, then show that a map g : R —› R defined by g(x) = x for x ∊ R is a bijective map.
(b) Let A = (1, 2, 3, 4) and
(1 2 3 4)
f= ( 2 4 1 3)
g = (1 2 3 4)
(4 1 2 3)
Find fog and gof.
(c) A club has 25 members. How many ways are there to choose four members of the
club to serve on an executive committee ?
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