BSc IT Sem III 2015 2016 2016 LDMS Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 Solve the following (any two) 10 marks
   • a) Define Induction. Prove by method of induction State and prove Additional principal & How many numbers in are multiple of 6 or 7?
   • c) With the help of truth table prove that equivalency
   • d) If A, B, are subset of U then prove that A x (B UC) & (A x B) U (Ax C) also give set
2. Q2 Solve the following (any two) - 10 marks
   • a) Let R be the equivalence relation of set A thenaR biff R(a) = 7 b) <) and (B <) are poset then (A X B, S) is a poset with partial order < defined by (a, b) a
   • d) Prove that (L is poset and check A = {2,3,6,12,24,36,72} is lattice Solve the following (any two) | (10) Define — i) Bijective function ii) Inverse function and find fog and gof if Define function,and prove it’s any, two properties
   • c) function f: A- B isan invertible then prove that it is bijective
   • d) State and prove Pigeon hole Principal with suitable example. Also state Extended Pigeon hole principal with example ) (ree and cheek the following Eulerian and
   • b) graph. Cheek following Bruphs are
   • i) il) y2 > ler and Left Data Right Construct tree and find value of tree. Also find pre-order, post order, Inorder g
   • d) Prove that the number of vericers of odd degree In even and draw all possible sp g tree of given graph
   • i) a ii) n b f
3. Q5 Solve any two. Show that prime residue classes modulo eleven with respect to multiplication modulo even 10 marks
   • b) Prove that (3, 6) is a group code if H = find minimum distance & how many e
   • c) i) Prove that every cyclic group is an abalian group
   • ii) Let G be a group ab G then prove that = a.& =
   • d) Let Z be a set of all even j n integers then show that semigroup (z +) and (T +) are isomorphic
4. Q6 Solve any two,
   • a) Find the solutio Relation by using genratring function if a, — + =
   • b) Find the soluti 100 Of Recurrncy Relation if Qn = — — =5, a, = —9,
   • c) Find the soluti of Recurrency Relation if dy = — + = 1,a,=3 ) ne Explicit formula and Implicit formula and Check {a} is solution of Recurrency Relation if Solve the following (any 3), (15) Show that R is an equivalence relation on set A iff (a,b) R, (a,c) R then (b,c)
   • b) Prove that w.r.t addition is an abalian group Let B, g:B C,h:C > D find (Fof)of (2), ( = + 2, g(b) = 3x,h(c) = 9x +5 and define composite function
   • d) Define L.H.R.R and find 7" term of R.R if a, = + + 3" = 1 : Apply the prims and Kruskal Algorithm. Find minimum weight of given diagram and Bare two sets then prove tha

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