Questionbanks  DSGT 
A quick guide to Bh.QuestionbanksBrainheaters Questionbanks is the collection of handpicked set of questions which are mostly repeated, important and recommended. Learning this set of questions can easily help you top or even just clear the exams. Given below are Expected Questionbanks for semester.
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MODULE1 1. Prove the following (AB)U(BA)=(A U B) (An B). 2. PROVE USING MATHEMATICAL INDUCTION 2+5+8+......+3(n1)=n(3n+1)/2 3. let A={a,b,c,d,e,f,g,h} Consider the following subsets of A A1={a,b,c,d} A2={a,c,e,g,h} A3={a,c 1 e,g} A4={b,d} A5={f,h} Determine whether following is partition of A or not. Justify i) {A1,A2} ii){A3,A4,A5} 4. In a class of students undergoing a computer course the following were observed Out of a total of 50 students. 30 know pascal 18 know Fortran 26 know COBOL 9 know both pascal and fortran 16 of them both Pascal and COBOL 8 know both fortran and cobol 47 know at least one of 3 languages For this we have to determine : 1) How many students know none of these languages 2) how many students know all three languages 3) how many students know exactly one language MODULE2 1. Determine the number of integers between 1 to 250 that are divisible by any integer 2,3,5,7. 2. Show that n(n21) is divisible by 24, where n is any odd positive integer. 3. Determine the following posets are boolean algebra. Justify your answer. i) A={1,2,3,6} with divisibility ii) D20: divisors of 20 with divisibility 4. Define universal and existential quantifiers? explain with examples. 5. Show that (~P^(~Q^R))V(Q^R)V(P^R)⇔R MODULE3 1. Suppose that A is non empty set, and f is a function that has A as its domain. Let R be the Relation on A consisting of all ordered pair (x,y) where f(x)=f(y) show that Ris an equivalence relation of A. 2. Given S={1,2,3,4} and a relation R on S given by R={(4,3),(2,2),(2,1),(3,1),(1,2)} i) show R is not transitive ii) Find transitive closure of R by warshall’s algorithm 3. Functions f,g,h are defined as a set X={1,2,3} f={(1,2),(2,3),(3,1)} , g{(1,2),(2,1),(3,3)} , h{(1,1),(2,1),(3,1)} i) Find f o g , g o f are they equal? ii) Find f o g o h and f o h o gv 4. Determine the matrix of partial order of visibility on the set A={1,3,5,15,30} Draw the Hasse diagram of the poset. Indicate whether it is a chain or not. 5. Find complement of each element in D30 6. Explain distributive Lattice show that the following diagrams represent nondistributive lattice. (Diagram) 7. Let the function f:RRf(x)=2x3 Find f2=f o f, f3=f o f 8. Let A be set of integers and R be the relation on AXA defined by(a,b)R(c,d) if and only if a+d=b+c. Prove that R is an equivalence relation. 9. Define reflexive closure and symmetric closure of a relation, Also find reflexive and symmetric Closure of R. A={1,2,3,4} R={(1,1),(1,2),(1,4),(2,4),(3,1),(3,2)(4,2),( 4,3),(1.4} MODULE4 1. find the ordinary generating functions for the given sequence: i) {0,1,2,3,4…} ii) {1,2,3,4…..} iii) {0,3,32,33,....} iv) {2,2,2,2,.....} 2. Define pigeonhole principle and extended pigeonhole principle show that if seven colours are used to paint 50 by cycles and at least 8 bicycles will be of same color. MODULE5 1. Prove that a connected graph with n vertices must have at least n1 edges. Can a single undirected graph of 8 vertices have 40 edges excluding self loop. 2. Let T be the set of even integers, show that (Z,+) and (T,+)are isomorphic. 3. Define Hamiltonian path and circuit with example what is the necessary and sufficient condition To exist Hamiltonian circuit? 4. Find the solution of ar+2+2ar+13ar=0 that satisfies a0=1, a1=2 5. Find the solution for ar+2+2ar+13ar=0 6. Decode the following words relative to a maximum spanning tree. use the same to find minimum tree for the following. (Diagram) 7. Define Euler's path i)Determine Euler cycle and path in graph in (a) ii)Determine Hamiltonian cycle and path in graph shown in (b). (Diagram) MODULE6 1. Consider the set A={1,2,3,4,5,6} under the multiplication modulo 7. i) find the multiplication table for above. ii) find the inverse of 2,3 and 5,6 iii) prove that it is a cyclic group iv) find the orders and the subgroups generated by{3,4}and {3,4}. 2. For each of the following sets of weights construct an optimal binary prefix code. For each weight. In the set give the corresponding code word: i) 1,2,4,6,9,10,12 ii)10,11,14,16,18,21 iii) 5,7,8,15,35,40. 3. Show that the (2,5) encoding functions e: B2B5 is defined by e(00)=00000 e(01)=01110 e(10)=10101 e(11)=11011 is a group code. How many errors will it detect? 4. prove that the set G ={0,1,2,3,4,5} is an abelian group of order 6 with respect to addition modulo 6. 5. consider the {3,5} group encoding function defined by 8e(000)=00000 e(001)=00110 e(010)=01001 e(011)=01111 e(100)=10011 e(101)=10101 e(110)=11010 e(111)=11000 6. Be a parity check matrix. Determine the group code group (Matrix) 7. Determine if following groups G1 and G2 are isomorphic or not. (Diagram) 
