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Discrete Mathematics

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Find transitive closure using Warshall's Algorithm.
discrete mathematics updated 3.8 years ago by pedsangini276 • 4.8k
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Determine whether the below Hasse diagram represents a lattice
discrete mathematics updated 3.8 years ago by pedsangini276 • 4.8k
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Let A = {1, 2, 3, 4, 5} and R be the relation defined by a R b if and only if a < b. Compute $R, R^2$ and $R^3$ .Draw digraph of $R, R^2$ and $R^3$.
discrete mathematics updated 3.8 years ago by pedsangini276 • 4.8k
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Let A={1,2,3,4,6}=B, a R b if and only if a is multiple of b. Find R. Find each of the Following (i) R(4) (ii) R(6) (iii) R({2,4,6}).
discrete mathematics updated 3.8 years ago by pedsangini276 • 4.8k
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Consider the chain of divisors of 4 and 9, i.e., $L_1$={1, 2, 4} and $L_2$={1, 3, 9}
discrete mathematics updated 3.8 years ago by pedsangini276 • 4.8k
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Frame the composition table
discrete mathematics updated 3.8 years ago by pedsangini276 • 4.8k
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Discrete Structures. Find the number of integers between 1 and 1000 which are (i) Divisible by 2,3 or 5 (ii) divisible by 3 only but not by 2 nor by 5
discrete mathematics updated 3.8 years ago by pedsangini276 • 4.8k
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Discrete Structures: Equivalence Relation
discrete mathematics updated 3.8 years ago by pedsangini276 • 4.8k
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Define distributive lattice. Show that in a bounded distributive lattice, if a complement exists, its unique.
discrete mathematics updated 3.8 years ago by pedsangini276 • 4.8k
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Consider the (3, 5) group encoding function
discrete mathematics updated 3.8 years ago by sagarkolekar ★ 11k
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Is it possible to draw a tree with five vertices having degrees 1, 1, 2, 2, 4?
discrete mathematics updated 3.8 years ago by sagarkolekar ★ 11k
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Prove that in a full binary tree with n vertices, the number of pendant vertices is (n+1)/2.
discrete mathematics updated 3.8 years ago by sagarkolekar ★ 11k
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If function f is an isomorphism from semigroup (S, *) to (T, *'), then prove that $f^{-1}$ ia an isomorphic from (T, *') to (S, *).
discrete mathematics updated 3.8 years ago by sagarkolekar ★ 11k
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Find the generating functions for the following sequence (i) 0, 0, 0, 1, 2, 3, 4, 5, 6, 7,............................. (ii) 6, -6, 6, -6, 6, -6, 6,...................
discrete mathematics updated 3.8 years ago by sagarkolekar ★ 11k
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Show that if any seven points am chosen in a regular hexagon whose sides are of 1 unit, then two of them must be no further apart than 1 unit.
discrete mathematics updated 3.8 years ago by sagarkolekar ★ 11k
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Determine the number of edges in a graph with 6 nodes, 2 nodes of degree 4 and 4 nodes of degree 2. Draw two such graphs.
discrete mathematics updated 3.8 years ago by sagarkolekar ★ 11k
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Determine whether following graphs are isomorphic
discrete mathematics updated 3.8 years ago by sagarkolekar ★ 11k
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Define isometric graphs. Show that following graphs are isomorphic.
discrete mathematics updated 3.8 years ago by sagarkolekar ★ 11k
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How many vertices are necessary to construct a graph with exactly 6 edges in which each vertex is of degree 2.
discrete mathematics updated 3.8 years ago by sagarkolekar ★ 11k
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Let the function f, g and h defined as follows: $f: R- > R, f(x)=2x+3\\ g:R- > R, g(x)=3x+4\\ h:R- > R, h(x)=4x \\ \text{Find gof, fog, foh, hof, gofoh}$
discrete mathematics updated 3.8 years ago by sagarkolekar ★ 11k
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Solve the recurrence relation $a_{r+2} -a_{r+1} -6a_r=4.$
discrete mathematics updated 3.8 years ago by sagarkolekar ★ 11k
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Find the generating function for the following series
discrete mathematics updated 3.8 years ago by pedsangini276 • 4.8k
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Find the generating function for the following sequence 1,2,3,4,5,6.........
discrete mathematics updated 3.8 years ago by pedsangini276 • 4.8k
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Find the generating function for the following sequence
discrete mathematics updated 3.8 years ago by pedsangini276 • 4.8k
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Find the solution to the recurrence relation $a_n=6a_{n-1}+11a_{n-2}-6a_{n-3}$ given $a_0=20,a_1=5 \ \ and \ \ a_2=15$
discrete mathematics updated 3.8 years ago by pedsangini276 • 4.8k
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