BSc IT Sem III 2014 2015 2015 LDMS Question Paper - Mumbai University | munotes

Questions asked in this paper

1. Q1 the following (Any Two)
   • b) Find and define Non- homogeneous R.R if by using generating function
   • d) Find explicit formula for = Land define explicit formula
2. Q2 Solve the following (Any Two) 10 marks
   • a) Ris relation onset A = a2, then prove
   • b) If R = (2,4)(2,5) then draw digraph, check equivvalence relation and give reasons and write inverse , of R & draw Hasse’s
   • c) - Let (A, R) is poset then show that (A, R~+) is poset
   • d) that (Dzq,/) is lattice and find LUB and GLB
3. Q3 Solve the following (Any Two) 10 marks
   • a) Define Bijective and every where define function and prove that fx) = is bijective function and find
   • b) Let be function such that gof =I, fog = Fis oneto one correspondence between B andA & each is inverse of other
   • d) Define characteistic function and prove any two properties the following (Any Two)
   • a) Prove that the number of vertices of odd degree in a graph is always even Define Euler graph, Path and circuit and check given digraphs are path,circuit & graph with explanation if that graphs are graph and Define ae find its value and Construct trée with the help of algebrale structure ahd tind Its draw Spanning tree of following
4. Q5 Solve the following (Any Two) Show that the set of all positive rational number forms an abelian group comp defined by as =
   • b) Define Semi Group and prove that (Z+) and (T+) lsomorphism
   • c) Define integral Domain & Prove that every field js an integral Domain but Converse is not true that e: B2 define is group with the help of following code CLG: Solve the following (Any Two)
   • a) mathematical Induction show that 12 6 (pV(~pVq)) = with truth table and define conditonal and
   • c) Prove that B are sets then A \ B= and define powerset with example
   • d) Define Sets and its types with suitable example and explain set identities
5. Q7 Solve the foliowing (Any Two) ; 15 marks
   • a) Solve by R.R using generating function method if + = 2" ,do =
   • b) Ris an equivalence relation on set Aiff (a,b) pairs in the relation R from A = {0,1,2,3,4,5} to B =
   • d) Solve the following min spanning of tree by Prims algorithm and Krushical algorithm
   • e) i) Define Cyclic and prove that (a+ isa ring w.r additio
   • ii) Let G & be isomorphic group if G is abelian then G js
   • f) state and prove additon principle with example

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