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Let ,$A=\{a, b\}$ and $A^2$ is the set of all words of length 2 i.e., $A^2=A x A$. (a). Find the element of $\mathrm{A}^2$.
discrete structures and graph theory updated 3.5 years ago by phenjoisilab • 0
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Prove that for any positive integer number $\mathrm{n}, \mathbf{n}^3+\mathbf{2} \mathbf{n}$ is divisible by 3 .
discrete structures and graph theory updated 3.5 years ago by phenjoisilab • 0
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Show that the group G = {1,2,3,4,5,6}x7 is cyclic. How many generators are there.
discrete structures and graph theory updated 3.5 years ago by thambisrilalith126 • 20
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Prove that, A non- empty subset $\mathrm{H}$ of a group $(\mathrm{G}, *)$ to be a subgroup is $\mathrm{a} \in \mathrm{H}, \mathrm{b} \in \mathrm{H} \rightarrow \mathrm{a}^* \mathrm{~b}^{-1}$...
discrete structures and graph theory updated 3.5 years ago by thambisrilalith126 • 20
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Prove that, If o(a)=n for some $a \in G$, then $a^m=e$ if n is a divisor of m.
discrete structures and graph theory updated 3.5 years ago by thambisrilalith126 • 20
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Four roots of unity form a finite abelian group with respect to multiplication.
discrete structures and graph theory updated 3.5 years ago by thambisrilalith126 • 20
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Let $f: R \rightarrow R$ be a function defined by $f(x)=p x+q$ for all $x \in R$. Also fof = I. Find the value of p and q.
discrete structures and graph theory updated 3.5 years ago by thambisrilalith126 • 20
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What do you mean by Functions and what are the different types of function explain briefly.
discrete structures and graph theory updated 3.5 years ago by thambisrilalith126 • 20
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Solve the following recurrence relation : $a_{r}-3 a_{r-1}=2, r \geq 1, a_{0}=1$
discrete structures and graph theory updated 3.9 years ago by thambisrilalith126 • 20
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Solve the recurrence relation,
discrete structures and graph theory updated 3.9 years ago by thambisrilalith126 • 20
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In equilibrium, A and B are in a horizontal line. If $ \angle B A C=\alpha \text { and } \angle A B C=\beta \text {, What is the ratio of } \tan \alpha: \tan \beta ? $
discrete structures and graph theory updated 3.9 years ago by thambisrilalith126 • 20
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If the line of action of the resultant of two forces P and Q divides the angle between them in the ratio 1 : 2, What is magnitude of the resultant?
discrete structures and graph theory updated 3.9 years ago by thambisrilalith126 • 20
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Find all spanning trees for the graph G pictured below.
discrete structures and graph theory updated 3.9 years ago by thambisrilalith126 • 20
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Solve the following recurrence relation : (i) $a_{r}-7 a_{r-1}+10 a_{r-2}=0$ given that $a_{0}=0$, $a_{1}=3$ (ii) $a_{r}-4 a_{r-1}+4 a_{r}-2=0$ given that $a_{0}=1$ and $a_{1}=6$
discrete structures and graph theory updated 3.9 years ago by thambisrilalith126 • 20
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If $A=\{1,2,3,4,5\}$ and $R=\{(1,2),(3,4),(4,5),(4,1),(1,1)\}$ find its transitive closure.
discrete structures and graph theory updated 3.9 years ago by thambisrilalith126 • 20
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Obtain disjunctive normal form of, i) $(p \rightarrow q) \wedge(\sim p \wedge q)$ ii) $(p \wedge(p \rightarrow q)) \rightarrow q$
discrete structures and graph theory updated 4.0 years ago by thambisrilalith126 • 20
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Find the shortest path between each pair of vertices for a simple graph using Warshall's algorithm.
discrete structures and graph theory updated 4.0 years ago by thambisrilalith126 • 20
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Find a root of $x^{4}-x^{3}+10 x+7=0$ correct up to three decimal places between $-2$ and $-1$ by Newten Raphson method.
discrete structures and graph theory updated 4.0 years ago by thambisrilalith126 • 20
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Find a root of the equation $x^{3}+x-1=0$ correct to three decimal places, by the method of False Position.
discrete structures and graph theory updated 4.0 years ago by thambisrilalith126 • 20
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Find a root of $x^{3}-x-1=0$ using Bisection methed correct to three decimal places.
discrete structures and graph theory updated 4.0 years ago by thambisrilalith126 • 20
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$ \text { If } C(n, 3)+C(n+2,3)=P(n, 3) \text {, find } n \text {. } $
discrete structures and graph theory updated 4.0 years ago by thambisrilalith126 • 20
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How many automobile license plates can be made if each plate contains taw different letters followed by three different digits. Solve the problem if the first digit can't be 0.
discrete structures and graph theory updated 4.0 years ago by thambisrilalith126 • 20
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a) Find the number of students staying in all three subjects. b) Find the number of students studying exactly one of the three subjects.
discrete structures and graph theory updated 4.0 years ago by thambisrilalith126 • 20
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How many integers between 1 to 2000 are divisible by 2, 3, 5 or 7?
discrete structures and graph theory updated 4.0 years ago by thambisrilalith126 • 20
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Define a binary operation *on the set $\{0,1,2,3,4,5\}$ as,
discrete structures and graph theory updated 4.0 years ago by thambisrilalith126 • 20
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