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)
   • a) Define Mathematical nduction. Prove by method of induction State and prove Additional princi ditional principal & How many numbers in are multiple of 6 or 72 With the help of p of truth table prove that
   • ii) = IfA, B, care subset of U th
2. Q2 Solve the following 10 marks
   • a) LetR the equivalence relation of set A then iff R(a) = R(b) (B <) are poset then (A x B, S) is a poset with partial order < defined by (a, b) = (a’ = a),(ab), (6.4), (b c), (be), (c a), (cc), e),(da),(d b), (dc), (d {(a c), (b b), (be), (c a), (c c), (cc), (da), a), (eb),
   • 4) Prove that is poset and check A = lattice
3. Q3 Solve the following (any Define Bijective function ti) Inverse function.and find 10 marks
   • b) Define function.and prove it’s any two properties q c) If function f: A > B is an 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
4. Q4 Solve the following (any two) tisfy Eulerian and thé following digraph
   • a) Define i) Graph ii) Minimal spanning tree and che Hamiltonian path, graph and circuit
   • b) Define Isomorphic graph. Check following graphs are isomorP Inorder and Left Data Right Construct tree and find value of tree. Also find pre-order, post order, Ino
   • d) Prove that the number of vericers of odd degree in a-group is even and draw all & that prime residue classes modulo eleven with respect to multiplication modulo
   • b) Prove that (3, 6) is a group code if H = find minimum distance & how many
   • c) 1) that every cyclic group is an abalian
   • ii) Let G bea G then prove that
   • d) Let Z bea set of all even integers then show that semigroup and (T +) are isomorphic
5. Q6 Solve any two
   • a) Find the solution of Recu : by using genratring function if a, + =
   • b) Find the solution of Re Find the solution of Recurrency Relation if an = — + =1 Define Explicit formula and Implicit formula and Check {a,,} is solution of Recurrency Relation
   • i) An = 0. = iii) An = 3.(2)" :
6. Q7 Solve the following (any {15} = Show that R is an equivalence relation onset A iff (a, b) R then (b,c) Prove that w.r.t addition is an abalian group y Let f:A > By giB > C,h:C > D find (2), ((hoh)og)(—3) if = 2 g(b) = 3x, h(c) 5 and define composite function @) Define L-H.R.R and find 7" term of RR = + = = = ~ e) Apply the Kruskal Algorithm. Find minimum weight of given diagram and B are two sets then prove that

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