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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 18 months ago by sagarkolekar ★ 11k
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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 18 months ago by sagarkolekar ★ 11k
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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 18 months ago by prajapatijaimin • 3.1k
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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 18 months ago by prajapatijaimin • 3.1k
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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 18 months ago by prajapatijaimin • 3.1k
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Four roots of unity form a finite abelian group with respect to multiplication.
discrete structures and graph theory updated 18 months ago by prajapatijaimin • 3.1k
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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 18 months ago by prajapatijaimin • 3.1k
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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 18 months ago by prajapatijaimin • 3.1k
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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 23 months ago by prajapatijaimin • 3.1k
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Solve the recurrence relation,
discrete structures and graph theory updated 23 months ago by prajapatijaimin • 3.1k
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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 23 months ago by prajapatijaimin • 3.1k
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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 23 months ago by prajapatijaimin • 3.1k
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Find all spanning trees for the graph G pictured below.
discrete structures and graph theory updated 23 months ago by prajapatijaimin • 3.1k
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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 23 months ago by prajapatijaimin • 3.1k
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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 23 months ago by prajapatijaimin • 3.1k
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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 23 months ago by prajapatijaimin • 3.1k
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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 23 months ago by prajapatijaimin • 3.1k
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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 23 months ago by prajapatijaimin • 3.1k
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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 23 months ago by prajapatijaimin • 3.1k
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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 23 months ago by prajapatijaimin • 3.1k
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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 23 months ago by prajapatijaimin • 3.1k
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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 23 months ago by prajapatijaimin • 3.1k
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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 23 months ago by prajapatijaimin • 3.1k
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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 23 months ago by prajapatijaimin • 3.1k
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Define a binary operation *on the set $\{0,1,2,3,4,5\}$ as,
discrete structures and graph theory updated 24 months ago by prajapatijaimin • 3.1k
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