# QP DM

Every year thousands of students appear for sppu exams, therefore it is very necessary for each and every student to be mentally prepared for the exams and for this case only we study the previous year question papers to get an insight of previous year question papers.

A good analysis of question papers can help you get a better head from others in the same exam as now you would be already prepared for those questions and that would even help you score better. The best advice that we can give you is that try to solve the maximum questions by yourself only rather than depending on solutions based books it would ultimately make your mind lazier and you will put effort much less and the result would be that you would get less out of the subjects.

These all are as per updated 2015 pattern onwards which are of 50 marks. The question paper is divided into 8 questions of which you have to attempt any four, there is a choice in every question,so among 1st two you have to attempt anyone and so on. The major advantage of this pattern is that it gives you the freedom to choose you among questions but each question comes with 12 to 13 marks per head so getting a question wrong in a subject where the start and final steps matter also count a lot.so we are also uploading a series of a specially designed question bank for better preparation.

QUESTION BANK

1) Obtain the conjunctive &disjunctive normal forms,
p∧(p→q) ii) ((p∨∼q)→q
2) Prove by mathematical induction, 2^n>n^3 for n≥10.
3) Define Power Set, Multiset, Multiplicity of an element in a multiset .If A={a,b,c}
then write P(A).
4) Obtain the disjunctive normal form,
i) (p→q)∧(∼p∧q). ii) (p∧(p→q))→q
5) Prove by mathematical induction for n≥1 ,1∙2+2∙3+ …+n(n+1)=(n(n+1)(n+2))/3
6) Draw the Hasse diagram,
Let R be a relation on set A , A ={2,3,4,6,8,12,38,48} defined by R ={(a,b)⁄a is divosor of b}
7) For the relation R={(1,2),(2,4),(1,3),(3,2)} on set A={1,2,3,4,5}
find the transitive closure using Warshall’s algorithm.
8) Draw the Hasse diagram for the following sets under the partial ordering relation
‘divides’ indicate those which are chains i) {2,4,12,24} ii){1,3,5,15,30}
9) Explain Pigeonhole Principal. Prove that if seven distinct numbers are
selected from {1, 2, . . . , 11},then some two of these numbers sum to 12.
10) A function f∶N⟶N where N is the set of natural numbers including zero.
Comment on the type of the following functions.
i) f(j)=j^2+2 ii) f(j) = 1 ; if j is odd
= 0 ; if j is even
11) For the relation R whose matrix is given find the matrix of transitive closure, using
Warshall’s algorithm.

12) Define Partial Ordering relation, Poset, Chain, Antichain .