Discrete Mathematics
Details
Download pdf| Question | Define Proposittion,Disjuntion, Conjuntion, Tautology and Contraposition | ||
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| 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. | ||
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| 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) | ||
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| NU Year | 2011 | ||
| Question | Define relation and function ? Write the properties of relation | ||
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| NU Year | 2011 | ||
| Question | Define handshaking theorem. Discuss graph rpresentation technique in memory | ||
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| NU Year | 2011 | ||
| Question | What is chromatic number of C6? Write necessary and sufficient conditions for Euler circuits and path | ||
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| NU Year | 2011 | ||
| Question | Prove that in an undirected graph even number of vertices of odd degree | ||
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| NU Year | 2011 | ||
| Question | What is planner graph? Are K3,3 and Q3 planner? | ||
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| 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 | ||
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| NU Year | 2011 | ||
| Question | State two basic counting principles and pigeonhole principle. | ||
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| 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)}? | ||
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| NU Year | 2011 | ||
| Question | How many bit strings of length eight start with a 1 bit or end with the 2 bits 00?? | ||
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| NU Year | 2011 | ||
| Question | What do you mean by graph coloring? write down it's some applications | ||
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| 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). zÌ„ | ||
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| NU Year | 2011 | ||
| Question | Define mathematical induction. Why mathematical induction is a valid proof technique? | ||
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| NU Year | 2011 2013 | ||
| Question | Use mathematical induction to show that- 1+2+22 +.......+2n = 2n+1 - 1 , for all non-negative integers n. | ||
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| 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 | ||
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| NU Year | 2011 | ||
| Question | What is spaning tree ? Show that a simple graph is connected if it has a spanning tree | ||
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| NU Year | 2011 | ||
19 Define Boolean expression and Boolean function. Find the sum-of-products expansion for the functi
| Question | Define Boolean expression and Boolean function. Find the sum-of-products expansion for the function ƒ(x,y,z) = (x+y) zÌ„ | ||
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| NU Year | 2011 | ||
| Question | Construct a half adder using logic gates | ||
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| NU Year | 2011 | ||
| Question | Prove the absorption law x(x+y) = x, using the order identities of Boolean algebra | ||
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| NU Year | 2011 | ||
| Question | Using Karnaugh maps to simplify the sum of products expressions, xȳz + xȳz̄ + x̄ yz + x̄ ȳz + x̄ ȳz̄ | ||
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| NU Year | 2011 | ||
| Question | Define propogation,Negation, Conjunction , Implications and Biconditional with examples | ||
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| NU Year | 2012 | ||
24 Which of the following sentences are propositions? What are truth value of those that are proposi
| 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 | ||
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| 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} | ||
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| 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? | ||
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| NU Year | 2012 | ||
| Question | Define mathematical induction? Use mathematical induction to prove that, n<2nfor all posetive integers n | ||
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| NU Year | 2012 | ||
| Question | Give an indirect proof of the theorem. "If 3n+2 is odd , then n is odd". | ||
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| NU Year | 2012 | ||
| Question | Define Fibonacci sequence. Find the Fibonacci numbers f2 f3 f4 f5 | ||
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| NU Year | 2012 | ||
| Question | Define rules of inference. Write down the basic steps of inference | ||
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| NU Year | 2012 | ||
| Question | Define mathematical induction why mathematical induction is a valid proof techinique? | ||
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| NU Year | 2012 | ||
| Question | Use mathematical induction to show that, 1 + 2 + 22+ ....... + 2n = 2n+1. | ||
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| NU Year | 2012 | ||
| Question | Give a big O estimate f(n) = 3n log (n!) + n2+3 ) log n, where n is appositive integer | ||
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| NU Year | 2012 | ||
| Question | Define graph, multigraph and pseudograph with example | ||
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| 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 | ||
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| NU Year | 2012 | ||
| Question | State two basic counting principles | ||
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| NU Year | 2012 | ||
| Question | How many bit string of length eight start with a 1 bit or end with the two bit 00? | ||
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| 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)}? | ||
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| 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? | ||
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| NU Year | 2012 | ||
| Question | Define Boolean expression and Boolean function. How many different Boolean functions of degree n are there? | ||
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| NU Year | 2012 | ||
| Question | What is the value of the postfix expression +-*235/1234? | ||
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| NU Year | 2012 | ||
| Question | Define Conjunction, Disjunction, Implication and Contrapositive with truth-table | ||
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| NU Year | 2013 | ||
| Question | Define relation and function. What are the properties of relation? | ||
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| 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) | ||
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| NU Year | 2013 | ||
| Question | Show the ¬(p∨(p∧q) and ¬p∧¬q logically equivalent. | ||
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| NU Year | 2013 | ||
| Question | Define rules of inference. Write down the basic rules of inference | ||
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| NU Year | 2013 | ||
| Question | Prove the theorem "The integer n is odd if and only if n2 is odd". | ||
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| 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. | ||
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| 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 | ||
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| NU Year | 2013 | ||