Discrete Mathematics
Question Define Proposittion,Disjuntion, Conjuntion, Tautology and Contraposition
NU Year 2011
Question Which of this sentence are proposition? Write true or false with cause:- (i) Birds can fly; (ii) Answer the question; (iii) 2+3=5; (iv) x+2=11; (v) 5+7=10.
NU Year 2011
Question Let A = {0,2,4,6,8}, B = {0,1,2,3,4} and C ={0,3,9,6} what are A∩B∩C and AU BUC? (Using Venn diagram and normal set theory)
NU Year 2011
Question Define relation and function ? Write the properties of relation
NU Year 2011
Question Define handshaking theorem. Discuss graph rpresentation technique in memory
NU Year 2011
Question What is chromatic number of C6? Write necessary and sufficient conditions for Euler circuits and path
NU Year 2011
Question Prove that in an undirected graph even number of vertices of odd degree
NU Year 2011
Question What is planner graph? Are K3,3 and Q3 planner?
NU Year 2011
Question (i) Prove the theorem. " The integer n is odd if and only if n2 is odd". (ii) Write properties of isomorphic graph
NU Year 2011
Question State two basic counting principles and pigeonhole principle.
NU Year 2011
Question What is the composite of the relations R and S where R is the relation form {1,2,3} to {1,2,3,4} with R = {(1,1),(1,4),(2,3),(3,1),(3,4)} and S is the relation from {1,2,3,4} to {0,1,2} with S = {(1,0),(2,0),(3,1),(3,2),(4,1)}?
NU Year 2011
Question How many bit strings of length eight start with a 1 bit or end with the 2 bits 00??
NU Year 2011
Question What do you mean by graph coloring? write down it's some applications
NU Year 2011
Question What do you mean by SOP and POS. Find the SOP expansion for the following function :- ƒ(x,y,z) = (x+y). z̄
NU Year 2011
Question Define mathematical induction. Why mathematical induction is a valid proof technique?
NU Year 2011 2013
Question Use mathematical induction to show that- 1+2+22 +.......+2n = 2n+1 - 1 , for all non-negative integers n.
NU Year 2011
Question Define one-to-one and onto function. Determine whether the function ƒ(x) =x2 fom the set of integers to the set of integers is one-to-one and onto
NU Year 2011
Question What is spaning tree ? Show that a simple graph is connected if it has a spanning tree
NU Year 2011
Question Define Boolean expression and Boolean function. Find the sum-of-products expansion for the function ƒ(x,y,z) = (x+y) z̄
NU Year 2011
Question Construct a half adder using logic gates
NU Year 2011
Question Prove the absorption law x(x+y) = x, using the order identities of Boolean algebra
NU Year 2011
Question Using Karnaugh maps to simplify the sum of products expressions, xȳz + xȳz̄ + x̄ yz + x̄ ȳz + x̄ ȳz̄
NU Year 2011
Question Define propogation,Negation, Conjunction , Implications and Biconditional with examples
NU Year 2012
Question Which of the following sentences are propositions? What are truth value of those that are propositions? (i) Comilla is the capital of Bangladesh (ii) Are you sick? (iii) x+1=3 (iv) What time is it? (v) 2+2=3
NU Year 2012
Question Show the Cartesian product B x A is not equal to the Cartesian product A x B where A={1,2} and B= {a,b,c}
NU Year 2012
Question Define Inverse function and Compositions of functions? Let f and g be the function from the set of integers to define by the f(x) = 2x+3 and g(x) = 3x+2 What is the composition of f and g? What is the composition of g and f?
NU Year 2012
Question Define mathematical induction? Use mathematical induction to prove that, n<2nfor all posetive integers n
NU Year 2012
Question Give an indirect proof of the theorem. "If 3n+2 is odd , then n is odd".
NU Year 2012
Question Define Fibonacci sequence. Find the Fibonacci numbers f2 f3 f4 f5
NU Year 2012
Question Define rules of inference. Write down the basic steps of inference
NU Year 2012
Question Define mathematical induction why mathematical induction is a valid proof techinique?
NU Year 2012
Question Use mathematical induction to show that, 1 + 2 + 22+ ....... + 2n = 2n+1.
NU Year 2012
Question Give a big O estimate f(n) = 3n log (n!) + n2+3 ) log n, where n is appositive integer
NU Year 2012
Question Define graph, multigraph and pseudograph with example
NU Year 2012
Question Draw the precedence graph for the following expression:- s1 : x : = 0 s2 : x : = x+1 s3 : y : = 2 s4 : z : = y s5 : x : = x+2 s6 : y : = x+z s7 : z : = 4
NU Year 2012
Question State two basic counting principles
NU Year 2012
Question How many bit string of length eight start with a 1 bit or end with the two bit 00?
NU Year 2012
Question What are the composite of the relation R and S, where R is the relation from {1,2,3} to {1,2,3,4} with R = {(1,1),(1,4),(2,3),(3,1),(3,4)} and S is the relation from {1,2,3,4} to with S = {(1,0),(2,0),(3,1),(3,2),(4,1)}?
NU Year 2012
Question Define binary relation. Consider the following relation on {1,2,3,4} :- R = {(1,1),(1,2),(1,4),(2,1),(2,2),(3,3),(4,1),(4,4)} Is the relation reflexive, symmetric and transitive?
NU Year 2012
Question Define Boolean expression and Boolean function. How many different Boolean functions of degree n are there?
NU Year 2012
Question What is the value of the postfix expression +-*235/1234?
NU Year 2012
Question Define Conjunction, Disjunction, Implication and Contrapositive with truth-table
NU Year 2013
Question Define relation and function. What are the properties of relation?
NU Year 2013
Question Let A={0,2,4,6,8}, B={0,1,2,3,4} and C= {0,3,6,9} what are A∩B∩C and AUBUC? (Using Venn diagram and normal set theory)
NU Year 2013
Question Show the ¬(p∨(p∧q) and ¬p∧¬q logically equivalent.
NU Year 2013
Question Define rules of inference. Write down the basic rules of inference
NU Year 2013
Question Prove the theorem "The integer n is odd if and only if n2 is odd".
NU Year 2013
Question Consider two sets A={1,2,3,4,5} and B= {1,3,5,7,9} (i) Find the bit strings of A an B; (ii) Use bit strings to find the union and intersection of these sets.
NU Year 2013
Question Suppose a graph G is presented by the following table:- G= [ x:y,z,w;y:x,y,w;z:z,w;w:z] (i) Find the number of vertices and edges in G. (ii) Are there any sources or sinks? (iii) Draw the graph of G
NU Year 2013