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Discrete Mathematics

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2
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R be a relation on set of integers Z defined by R = {(x, y) | x-y is divisible by 3} Show that R is an equivalence relation and describe the equivalence classes.
discrete mathematics updated 2.2 years ago by sagarkolekar ★ 11k
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24k
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Draw its Hasse diagram. P(A) is the power set of A.
discrete mathematics updated 2.2 years ago by sagarkolekar ★ 11k
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70k
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Prove that the set G = (1, 2, 3, 4, 5, 6) is an abelian group under multiplication modulo 7.
discrete mathematics updated 2.2 years ago by sagarkolekar ★ 11k
3
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9.3k
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Find the complement of each element in D30
discrete mathematics updated 2.4 years ago by sagarkolekar ★ 11k
6
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37k
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Draw Hasse Diagram of $D_{42}$, Find the complement of each element in $D_{42}$.
discrete mathematics updated 2.4 years ago by sagarkolekar ★ 11k
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9.7k
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$\text{Find the generating function for the following finite sequences} \\1. \ \ \ \ 1, 1, 1, 1, 1, 1,......$
discrete mathematics updated 2.4 years ago by sagarkolekar ★ 11k
0
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2.4k
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1
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Determine the group code
discrete mathematics updated 2.6 years ago by pedsangini276 • 4.8k
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1.7k
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Write short note on growth of functions.
discrete mathematics updated 2.7 years ago by Krishna_Agrawal • 2.7k
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Define isomorphism of graphs. find if the following two graphs are isomorphic. if yes find one to one correspondence between the vertices.
discrete mathematics updated 2.7 years ago by pedsangini276 • 4.8k
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654
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If, $ f(x)=x, \quad 0<x<\frac{\pi}{2} $ $ =\pi-x, \quad \frac{\pi}{2}<x<\pi $ show that, (i) $f(x)=\frac{4}{\pi}\left[\sin x-\frac{\sin 3 x}{3^{2}}+\frac{\sin 5 x}{5^{2}}-\ldots \ldots\right]$
discrete mathematics updated 2.7 years ago by prajapatijaimin • 3.3k
0
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580
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Find the normals to the ellipse $x^{2} / 9+y^{2} / 4=1$ which are farthest from its centre.
discrete mathematics updated 2.7 years ago by prajapatijaimin • 3.3k
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499
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If $\alpha=e^{2 \pi i / 7}$ and $f(x)=A_{0}+\sum_{k=1}^{20} A_{k} x^{k} \\$, then find the value of, $f(x)+f(\alpha x)+\ldots+f\left(\alpha^{6} x\right)$ independent of $\alpha .$
discrete mathematics updated 2.7 years ago by prajapatijaimin • 3.3k
0
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Draw the Hasse diagram of the following sets under the partial order relation divides and indicate which are chains. justify your answer.
discrete mathematics updated 2.7 years ago by sagarkolekar ★ 11k
1
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4.4k
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1
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Find got, fog, foh, gofoh.
discrete mathematics updated 2.8 years ago by sagarkolekar ★ 11k
0
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1.9k
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Question based on pigeonhole principle
discrete mathematics updated 2.9 years ago by Krishna_Agrawal • 2.7k
1
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30k
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A survey of 500 television watchers produced the following information:
discrete mathematics updated 2.9 years ago by pedsangini276 • 4.8k
2
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23k
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Consider the group G = (1,2,3,4,5,6) under multiplication modulo 7 a) Find multiplication table of G b) find Inverse of every element
discrete mathematics updated 2.9 years ago by pedsangini276 • 4.8k
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Let H= $\begin{bmatrix} 1&0&0 \\ 1&1&0 \\ 0&1&1 \\ 1&0&0 \\ 0&1&0 \\ 0&0&1 \end{bmatrix}$ be parity check matrix.
discrete mathematics updated 2.9 years ago by sagarkolekar ★ 11k
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Show that if every element in a group is its own inverse, then the group must be abelian.
discrete mathematics updated 2.9 years ago by sagarkolekar ★ 11k
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Let G={1, 2, 3, 4, 5, 6}. Prove that $(G, x_7)$ is a finite Abelian group with respect to multiplication modulo 7.
discrete mathematics updated 2.9 years ago by sagarkolekar ★ 11k
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Let H= $\begin{bmatrix} 1&0&0 \\ 1&1&0 \\ 0&1&1 \\ 1&0&0 \\ 0&1&0 \\ 0&0&1 \end{bmatrix}$ be parity check matrix.Determine the group code $e_H: B^2->B^5$
discrete mathematics updated 2.9 years ago by pedsangini276 • 4.8k
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1.3k
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Show that a group G is Ablian, if and only if $(ab)^2 = a^2 b^2$ for all elements a and b in G
discrete mathematics updated 2.9 years ago by pedsangini276 • 4.8k
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Show that the (2, 5) encoding function e: $B^2-> B^5$ defined by e(00) = 00000 e(01) = 01110 e (10) = 10101 e (11) = 11011 is a group code. How many errors will it detect and correct?
discrete mathematics updated 2.9 years ago by pedsangini276 • 4.8k
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Prove that the set A= {0,1,2,3,4,5} is a finite Abelian group under addition modulo 6.
discrete mathematics updated 2.9 years ago by pedsangini276 • 4.8k
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Define group, monoid, semigroup.
discrete mathematics updated 2.9 years ago by pedsangini276 • 4.8k
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