Partial preview of the text
Download B.Tech. Semester 3 Discrete Maths PYQs and more Papers Discrete Mathematics in PDF only on Docsity!
=> ooo piease wrtte your Exam Rott No) Bram Rott No ia Enp TERM EXAMINATION ‘Turrn SEMESTER [B.TECH] DECEMBER 2024 y _Tamn SexEs1 eR State and prove Coset Lagronge's theorem, Code CIC205 ‘Subject Discrete Mathamagy ae Age homomorphism and tsomo¢phism with example my Timer 3 Hours —_ Meskimiam Hares ~W] prove that Z+ = (0, 1, 2, 3 is an abelian group with wane 2) or mation al lidine ©. 3 Kes: 6 L Broup with respect t¢ Note: Attempt five questions tn all including Q. No.1 which te oo ‘modulo 4. pect to addition compulsory. Select one question from cach untt, Assume missing at a | any. a vuntrav —_— oe Q8 [a] State and prove five color theorem. ‘sy Are a a omatie numberof graph with example {9x5~20) 1 Peers ave 20 venoes each ef eres 3 ne ay est A Bec te contaposiine of he statement AF John isa poet, then docs a vepresentaton ofthis planer paph gts fans eens he is poor.” “ne 4 sedi 1c und prove Buler's formula, {a\Desine cyclic permutation. Give an example. begs fay State and pr : GG) Disterentiate between oriented and unoriented graph, _ 2° Ef Explain BFS algorithm in deta with a sutabie example a (ey Shows that (Pag) > (pv g)is tautology. 4 oo UNIT-I rreeties 4S (a) Define the following term with the help of an example: ia “ (i) Equality of set (ii) Power set (ii) Equivalent set, liv) Disjoint set (v) Shows that the premises “A student in the class has not read the oak” and “everyone in the class passed the first exam® implies the conclusion “someone who passed the first exam has not read the book” he Q3 {a} Using proof of contrapasitive prove that "if sye (set of integer) such that xy is odd then both xand y are odd. 6) (b) State and prove the principle of inclusion and exclusion for n number /- of set. (5) 5 UNIT-IT se je Prove that a given set B-{1, 2, 3, 5, 30) is lattice for the given condition “is divisible by”. (4) 1 LpBratuate the condition of function to be: (3) | ii) injective (af Surjective ) Bijective j ind out the sequence generated by the recurrence relation Ty = 2Tn1 ; with 7; = 4linitial condition). 3) QS (a) Minimize the given function using K-map (5) [ ABCD+ ABCD + ABCD+ ABCD + ABCD + ABCD + ABCD | (b) For the first order linear recurrence relation, proved that ae =e" as (5) { UNIT-II ; | Q6 a) Let G be the set of all positive rational number and * be the binary operation on G define by a*b = ab/7 for alla,beG. Prove that (G,")is j an abelian group. is) (0) Find the all coset of = (0, 4} in the group G= (Za, +e) 6) P.T.O. 2 1, A-/2 & isos cIt-don 
