Mathematics-B.C.A-OCT-2019

Name   …………………………… Roll No ……………………….

SAINTGITS COLLEGE OF APPLIED SCIENCES

MODEL INTERNAL ASSESSMENT EXAMINATION, OCTOBER 2019

Department of BCA      , Semester I(Answer key)

DISCRETE MATHEMATICS I

Total   : 80 marks                                                                        Time:3 Hours

1. Draw directed graph

2.A relation which is reflexive, symmetric and transitive is called equivalence relation.

3.In Z⁺ the relation ≤ is symmetric.

4.If p is prime and a is an integer not divisible by p then a^p-1 is congruent to 1 mod p.

5.Let a be an integer d a positive integer. Then there are unique integers q and r with 0≤r<d such that a=dq+r

6.A function is called increasing if f(x)≤f(y) when x<y, and decreasing if f(x)≥f(y) , x<y

7.Not true. example x,y=

8.-=297925

9.Let m₁, m₂,……m_n be pairwise relatively  prime positive integers a_1,a₂………a_n arbitrary integers Then the system x congruent to a₁(mod m1)……… x congruent to a_n(mod m_n) has a unique solution.

10.Disjuctive syllogism

11.Collection of all subsets of a set is called power set.  2³

12.A compound proposition that is always true is called tautology.

                                                                                                                       

13.

14. 18=4. 252-5. 198

15.Draw graph

16. sa+tb=1, sac+tbc=c then by theorem a/c.

17.S=  , rS=  S+(a)

18.f(x)  x<y,   <  , g(x)g(y)

19.Draw truth table.

20.n=a.b   ,then prove a b

21.write the definition of conjunction, disjunction, and negation.

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22.Assume R is transitive and by induction method prove RⁿcR .Conversely  assume  and prove transitive.

23.Let M_k=,  Mk yk=1(mod mk),  x=a₁M₁y₁+ a₂M₂y2+……….. a_nM_nyn is a solution.

24.  a/b,  b=as  and a/c, c=at then prove.

25.       case (i)0≤<     case (ii) <≤1 prove theorem

                                                                       

                                                                                                                       

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