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3
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21k
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Functions f, g, h are defined on a set, X= {1,2,3} as f= {(1,2) (2,3) (3,1)} g = {(1,2} (2,1) {3,3)) h = {(1, 1 ) (2,2) (3,1)} (i) Find fog, g o f are they equal ? (ii) Find fogoh and fohog.
discrete mathematics updated 4.2 years ago by krithikkm200 • 10
3
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23k
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Find the generating function for the following sequence 1,2,3,4,5,6.........
discrete mathematics updated 4.3 years ago by krithikkm200 • 10
2
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40k
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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 4.3 years ago by phenjoisilab • 0
2
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1000
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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 4.0 years ago by thambisrilalith126 • 20
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886
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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 4.0 years ago by thambisrilalith126 • 20
0
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927
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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 4.0 years ago by thambisrilalith126 • 20
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2.2k
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Write short note on growth of functions.
discrete mathematics updated 4.0 years ago by yerasylmakulbe671 • 10
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21k
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How many symmetric and reflexive relations are there on a set with n elements?
discrete mathematics updated 4.3 years ago by phenjoisilab • 0
4
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8.8k
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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 4.3 years ago by krithikkm200 • 10
2
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1.9k
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Consider the region shown below. It is bounded by a regular hexagon whose sides are the length 1 units.
discrete mathematics updated 4.3 years ago by phenjoisilab • 0
3
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Discrete Structures: Equivalence Relation
discrete mathematics updated 4.3 years ago by krithikkm200 • 10
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2.6k
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Question based on pigeonhole principle
discrete mathematics updated 4.2 years ago by yerasylmakulbe671 • 10
0
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1
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1.6k
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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 4.3 years ago by krithikkm200 • 10
0
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1.0k
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If f:$A \rightarrow B$ be both one-to-one and onto, the prove that $f^{-1}: B \rightarrow A$ is also both one-to-one and onto.
discrete mathematics updated 4.3 years ago by krithikkm200 • 10
0
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1.3k
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Use the laws of logic to show that $[(p \rightarrow q) \hat \ \ \ \sim q]\rightarrow \sim p$ is tautology.
discrete mathematics updated 4.3 years ago by krithikkm200 • 10
0
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1
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1.3k
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1
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Show that $A \times (B \cap C) = (A \times B) \cap (A \times C)$
discrete mathematics updated 4.3 years ago by krithikkm200 • 10
0
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12k
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Find how many integers between 1 and 60 are (i) not divisible by 2 nor by 3 and nor by 5. (ii) Divisible by 2 but not by 3 and nor by 5.
discrete mathematics updated 4.3 years ago by krithikkm200 • 10
1
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30k
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A survey of 500 television watchers produced the following information:
discrete mathematics updated 4.2 years ago by krithikkm200 • 10
0
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1.9k
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Show that $A-(B-C)=(A-B) \cup ( A \cap B \cap C)$
discrete mathematics updated 4.3 years ago by krithikkm200 • 10
0
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3.9k
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It was found that in a class, 80 students are passed in English, 60 in Science and 50 in Mathematics. It was also found that 30 students passed in both English and Science, 15 students passed in both
discrete mathematics updated 4.3 years ago by krithikkm200 • 10
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5.5k
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If 11 people are chosen from a set of A=(1, 2, 3, . . . 20), then one of them is multiple of other.
discrete mathematics updated 4.3 years ago by krithikkm200 • 10
1
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1
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8.7k
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Find how many integers between 1 and 60 are not divisible by 2 nor by 3 and nor by 5 respectively.
discrete mathematics updated 4.3 years ago by krithikkm200 • 10
0
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1.3k
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Prove by mathematical induction $^n-y^n$ is divisible by x-y.
discrete mathematics updated 4.3 years ago by krithikkm200 • 10
2
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16k
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Prove that $8^n - 3^n$ is a multiple of 5 by mathematical Induction, n>=1.
discrete mathematics updated 4.3 years ago by krithikkm200 • 10
0
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Use the laws of logic to determine the following expression as tautology or contradiction.
discrete mathematics updated 4.3 years ago by krithikkm200 • 10
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