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BC0052-Fall_Drive-Assignment-2011 - (Book ID B0972...

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Fall 2011 Bachelor of Computer Application (BCA) Semester 5 BC0052 Theory of computer science 4 Credits (Book ID: B0972) Assignment Set 1 (60 Marks) Answer the following questions 10 6 = 60 1. Show that the relation ) (mod m b a is an equivalence relation. 2. Using the definition of order show that 1 2 2 x x is ) ( 2 x O . 3. Prove by the method of contradiction that 2 is not a rational number. 4. Prove by mathematical induction 6 ) 1 2 )( 1 ( ....... 3 2 1 2 2 2 2 n n n n 5. Prove that “The sum of the degrees of the vertices of a graph G is twice the number of edges” 6. Prove that T is a tree there is one and only one path between ev ery pair of vertices”
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Fall 2011 Bachelor of Computer Application (BCA) Semester 5 BC0052 Theory of computer science 4 Credits
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Unformatted text preview: (Book ID: B0972) Assignment Set – 1 (60 Marks) Answer the following questions 10  6 = 60 1. Prove that “A tree G with n vertices has (n–1) edges” 2. If ) }, , 1 { }, 1 , { }, ({ S G     then find L(G), the language generated by G. 3. Obtain a DFA to accept strings of a’s and b’s starting with the string ab. 4. Briefly describe Moore and Mealy machines. 5. Draw the state diagram for the finite automation M = (Q,  , q ,  , F) where  = {a, b}, Q = {q , q 1 , q 2 }, F = {q , q 1 },  : Q    Q defined by 6. Obtain a regular expression such that    } 1 , { / { ) ( w R L } with atleast three consecutive 0’s.  a b q q q 1 q 1 q q 2 q 2 q 2 q 2...
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