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4
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1
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4.9k
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1
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Consider a set of integers from 1 to 250.
discrete structures and graph theory updated 2.1 years ago by prajapatijaimin • 3.1k
6
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425
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Relation and fuction
discrete structures and graph theory updated 2.1 years ago by prajapatijaimin • 3.1k
3
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338
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In each of the following cases, state whether the function is one-one, onto or bijective. Justify your answer.
discrete structures and graph theory updated 2.0 years ago by prajapatijaimin • 3.1k
2
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383
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1
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Consider $f:\{1,2,3\} \rightarrow\{a, b, c\}$ given by $f(1)=a, f(2)=b$ and $f(3)=c$. Find $f^{-1}$ and show that $\left(f^{-1}\right)^{-1}=f$.
discrete structures and graph theory updated 2.0 years ago by prajapatijaimin • 3.1k
2
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364
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Define a binary operation *on the set $\{0,1,2,3,4,5\}$ as,
discrete structures and graph theory updated 2.0 years ago by prajapatijaimin • 3.1k
2
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3.2k
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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 2.0 years ago by prajapatijaimin • 3.1k
2
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1
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414
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Show that function $f: \mathbf{R} \rightarrow\{x \in \mathbf{R}:-1<x<1\}$ defined by $f(x)=\frac{x}{1+|x|}, x \in \mathbf{R}$ is one-one and onto function.
discrete structures and graph theory updated 2.0 years ago by prajapatijaimin • 3.1k
2
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352
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Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be defined as $f(x)=10 x+7$. Find the function $g: \mathbf{R} \rightarrow \mathbf{R}$ such that $g$ o $f=f$ $\circ g=1_{\mathbf{R}}$.
discrete structures and graph theory updated 2.0 years ago by prajapatijaimin • 3.1k
4
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312
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1
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Show that $f$ is invertible with the inverse $f^{-1}$ of given $f$ by $f^{-1}(y)=\sqrt{y-4}$ where $\mathbf{R}_{+}$is the set of all non-negative real numbers.
discrete structures and graph theory updated 2.0 years ago by prajapatijaimin • 3.1k
3
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1
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312
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1
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Show that $f:[-1,1] \rightarrow \mathbf{R}$, given by $f(x)=\frac{x}{(x+2)}$ is one-one. Find the inverse of the function $f:[-1,1] \rightarrow$ Range $f$.
discrete structures and graph theory updated 2.0 years ago by prajapatijaimin • 3.1k
2
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327
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Consider $f: \mathbf{R}_{+} \rightarrow[-5, \infty)$ given by $f(x)=9 x^{2}+6 x-5 .$ Show that $f$ is invertible with $ f^{-1}(y)=\left(\frac{(\sqrt{y+6})-1}{3}\right) $
discrete structures and graph theory updated 2.0 years ago by prajapatijaimin • 3.1k
3
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1
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947
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What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5?
discrete structures and graph theory updated 2.0 years ago by prajapatijaimin • 3.1k
2
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1
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295
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1
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Find the area of the region lying inside, $ \begin{aligned} x^{2}+(y-1)^{2} &=1 \text { and outside,} \\\\ c^{2} x^{2}+y^{2} &=c^{2} \text { where } c=(\sqrt{2}-1) \end{aligned} $
discrete structures and graph theory updated 2.0 years ago by prajapatijaimin • 3.1k
0
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386
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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
0
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572
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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 24 months ago by prajapatijaimin • 3.1k
0
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331
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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 24 months ago by prajapatijaimin • 3.1k
0
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1
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402
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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 2.0 years ago by prajapatijaimin • 3.1k
1
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1
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1.1k
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1
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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 2.0 years ago by prajapatijaimin • 3.1k
1
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1
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2.4k
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1
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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 2.0 years ago by prajapatijaimin • 3.1k
0
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1
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6.9k
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1
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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 2.0 years ago by prajapatijaimin • 3.1k
0
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1
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365
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1
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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 2.0 years ago by prajapatijaimin • 3.1k
0
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1
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301
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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 2.0 years ago by prajapatijaimin • 3.1k
0
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446
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1
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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 2.0 years ago by prajapatijaimin • 3.1k
0
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1.7k
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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 2.0 years ago by prajapatijaimin • 3.1k
1
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1
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329
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1
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Let f, g and h be functions from R to R. Show that,
discrete structures and graph theory updated 2.0 years ago by prajapatijaimin • 3.1k
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