Discrete Mathematics

Details

#### 1 Define Proposittion,Disjuntion, Conjuntion, Tautology and Contraposition

Question Define Proposittion,Disjuntion, Conjuntion, Tautology and Contraposition 2011

#### 2 Which of this sentence are proposition? Write true or false with cause:- (i) Birds can fl

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. 2011

#### 3 Let A = {0,2,4,6,8}, B = {0,1,2,3,4} and C ={0,3,9,6} what are A&cap;B&cap;C and AU BUC? (Using V

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) 2011

#### 4 Define relation and function ? Write the properties of relation

Question Define relation and function ? Write the properties of relation 2011

#### 5 Define handshaking theorem. Discuss graph rpresentation technique in memory

Question Define handshaking theorem. Discuss graph rpresentation technique in memory 2011

#### 6 What is chromatic number of C6? Write necessary and sufficient conditions for Euler ci

Question What is chromatic number of C6? Write necessary and sufficient conditions for Euler circuits and path 2011

#### 7 Prove that in an undirected graph even number of vertices of odd degree

Question Prove that in an undirected graph even number of vertices of odd degree 2011

#### 8 What is planner graph? Are K3,3 and Q3 planner?

Question What is planner graph? Are K3,3 and Q3 planner? 2011

#### 9 (i) Prove the theorem. " The integer n is odd if and only if n2 is odd".

Question (i) Prove the theorem. " The integer n is odd if and only if n2 is odd". (ii) Write properties of isomorphic graph 2011

#### 10 State two basic counting principles and pigeonhole principle.

Question State two basic counting principles and pigeonhole principle. 2011

#### 11 What is the composite of the relations R and S where R is the relation form {1,2,3} to {1,2,3,4}

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)}? 2011

#### 12 How many bit strings of length eight start with a 1 bit or end with the 2 bits 00??

Question How many bit strings of length eight start with a 1 bit or end with the 2 bits 00?? 2011

#### 13 What do you mean by graph coloring? write down it's some applications

Question What do you mean by graph coloring? write down it's some applications 2011

#### 14 What do you mean by SOP and POS. Find the SOP expansion for the following function :- &fn

Question What do you mean by SOP and POS. Find the SOP expansion for the following function :- ƒ(x,y,z) = (x+y). z̄ 2011

#### 15 Define mathematical induction. Why mathematical induction is a valid proof technique?

Question Define mathematical induction. Why mathematical induction is a valid proof technique? 2011 2013

#### 16 Use mathematical induction to show that- 1+2+22 +.......+2n = 2

Question Use mathematical induction to show that- 1+2+22 +.......+2n = 2n+1 - 1 , for all non-negative integers n. 2011

#### 17 Define one-to-one and onto function. Determine whether the function &fnof;(x) =x2

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 2011

#### 18 What is spaning tree ? Show that a simple graph is connected if it has a spanning tree

Question What is spaning tree ? Show that a simple graph is connected if it has a spanning tree 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) z̄ 2011

#### 20 Construct a half adder using logic gates

Question Construct a half adder using logic gates 2011

#### 21 Prove the absorption law x(x+y) = x, using the order identities of Boolean algebra

Question Prove the absorption law x(x+y) = x, using the order identities of Boolean algebra 2011

#### 22 Using Karnaugh maps to simplify the sum of products expressions, xȳz + xȳ

Question Using Karnaugh maps to simplify the sum of products expressions, xȳz + xȳz̄ + x̄ yz + x̄ ȳz + x̄ ȳz̄ 2011

#### 23 Define propogation,Negation, Conjunction , Implications and Biconditional with examples

Question Define propogation,Negation, Conjunction , Implications and Biconditional with examples 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 2012

#### 25 Show the Cartesian product B x A is not equal to the Cartesian product A x B wh

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} 2012

#### 26 Define Inverse function and Compositions of functions? Let f and g be the function from

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? 2012

#### 27 Define mathematical induction? Use mathematical induction to prove that, n&lt;2n

Question Define mathematical induction? Use mathematical induction to prove that, n<2nfor all posetive integers n 2012

#### 28 Give an indirect proof of the theorem. "If 3n+2 is odd , then n is odd".

Question Give an indirect proof of the theorem. "If 3n+2 is odd , then n is odd". 2012

#### 29 Define Fibonacci sequence. Find the Fibonacci numbers f2 f3

Question Define Fibonacci sequence. Find the Fibonacci numbers f2 f3 f4 f5 2012

#### 30 Define rules of inference. Write down the basic steps of inference

Question Define rules of inference. Write down the basic steps of inference 2012

#### 31 Define mathematical induction why mathematical induction is a valid proof techinique?

Question Define mathematical induction why mathematical induction is a valid proof techinique? 2012

#### 32 Use mathematical induction to show that, 1 + 2 + 22+ ....... + 2n =

Question Use mathematical induction to show that, 1 + 2 + 22+ ....... + 2n = 2n+1. 2012

#### 33 Give a big O estimate f(n) = 3n log (n!) + n2+3 ) log n, where n is appositiv

Question Give a big O estimate f(n) = 3n log (n!) + n2+3 ) log n, where n is appositive integer 2012

#### 34 Define graph, multigraph and pseudograph with example

Question Define graph, multigraph and pseudograph with example 2012

#### 35 Draw the precedence graph for the following expression:- s1 : x : = 0

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 2012

#### 36 State two basic counting principles

Question State two basic counting principles 2012

#### 37 How many bit string of length eight start with a 1 bit or end with the two bit 00?

Question How many bit string of length eight start with a 1 bit or end with the two bit 00? 2012

#### 38 What are the composite of the relation R and S, where R is the relation from {1,2,3} to {1,

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)}? 2012

#### 39 Define binary relation. Consider the following relation on {1,2,3,4} :- R = {(1,1),(1,2)

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? 2012

#### 40 Define Boolean expression and Boolean function. How many different Boolean functions of degree n

Question Define Boolean expression and Boolean function. How many different Boolean functions of degree n are there? 2012

#### 41 What is the value of the postfix expression +-*235/1234?

Question What is the value of the postfix expression +-*235/1234? 2012

#### 42 Define Conjunction, Disjunction, Implication and Contrapositive with truth-table

Question Define Conjunction, Disjunction, Implication and Contrapositive with truth-table 2013

#### 43 Define relation and function. What are the properties of relation?

Question Define relation and function. What are the properties of relation? 2013

#### 44 Let A={0,2,4,6,8}, B={0,1,2,3,4} and C= {0,3,6,9} what are A&cap;B&cap;C and

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) 2013

#### 45 Show the &not;(p&or;(p&and;q) and &not;p&and;&not;q logically equivalent.

Question Show the ¬(p∨(p∧q) and ¬p∧¬q logically equivalent. 2013

#### 46 Define rules of inference. Write down the basic rules of inference

Question Define rules of inference. Write down the basic rules of inference 2013

#### 47 Prove the theorem "The integer n is odd if and only if n2 is odd".

Question Prove the theorem "The integer n is odd if and only if n2 is odd". 2013

#### 48 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;

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. 2013

#### 49 Suppose a graph G is presented by the following table:- G= [ x:y,z,w;y:x,y,w;z:z,w;w:z]

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 2013 