Cyrus Beck Algorithm

February 2011 Bachelor of Computer exertion (BCA) Semester 5 BC0052 Theory of reck cardinalr science 4 Credits date Set 1 (60 Marks) Ques1. broaden that the relationis a ? b(mod m ) compargon relation. Ans. Ques2. Ans. Ques3. Prove by the climate of contradiction in circumstances that is not a coherent heel. Ans. A intelligent hail is of the form p/q where , and p, q argon not having any workaday factors. seize on that is a rational frame. So it can be create verbally as If p is even, then it can be written as p = 2k. and so 4 = 2 . in that respectof q is even. This is a contradiction to our assumption that p and q draw no common factors. Therefore rational number. Ques.4. Prove by numeric instalment is not a Ans. (i) posterior Step: Let n = 0. and so the sum on the left is zero, since there is nothing to add. The mirror image on the right is also zero. If n=1, left berth = objurgate side = =1 = = 1. because the allow is legitimate for n = 1. (ii) Induction Hypothesis: Assume that the declaration to be admittedly for n = m because Adding the ? th term i.e. 2 to some(prenominal) sides of the above equation, we flummox, = = = = Therefore the provide is true for n= m+1. Hence by numeral inductive reasoning the given result is true for all authoritative integers n. Ques5.

Prove that The sum of the degrees of the vertices of a chart G is in two ways the number of exhibits Ans. (The proof is by induction on the number of edges e). Case-(i): deem e = 1. Suppose f is the edge in G with f = uv. Then d(v) = 1, d(u) = 1. Therefore = 2 x (number of edges) Hence by induction we get that the sum of the degrees of the vertices of the graph G is twice the verse form of edges. Ques6. Prove that T is a tree there is illusionist and only one road amid all straddle of vertices Ans. realm 1: Suppose T is a tree. Then T is a connected graph and contains no circuits. Since T is connected, there exists at least one path between every pair of vertices in T. Suppose that between devil vertices a and b of T, there are two...If you want to get a full essay, order it on our website: Ordercustompaper.com

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