The question is

"Suppose R and S are relations on a set A. If R and S are reflexiverelations, then $R\circ S$ is reflexive" select true or false.

Bernard Boyer
2022-07-15
Answered

$R\circ S$I have only seen this circle operator with function compositions, so is this "Set Composition"? If so, then how does it work?

The question is

"Suppose R and S are relations on a set A. If R and S are reflexiverelations, then $R\circ S$ is reflexive" select true or false.

The question is

"Suppose R and S are relations on a set A. If R and S are reflexiverelations, then $R\circ S$ is reflexive" select true or false.

You can still ask an expert for help

asked 2020-11-09

Use proof by Contradiction to prove that the sum of an irrational number and a rational number is irrational.

asked 2021-08-02

Suppose that A is the set of sophomores at your school and B is the set of students in discrete mathematics at your school. Express each of these sets in terms of A and B.

a) the set of sophomores taking discrete mathematics in your school

b) the set of sophomores at your school who are not taking discrete mathematics

c) the set of students at your school who either are sophomores or are taking discrete mathematics

Use these symbols:$\cap \cup$

a) the set of sophomores taking discrete mathematics in your school

b) the set of sophomores at your school who are not taking discrete mathematics

c) the set of students at your school who either are sophomores or are taking discrete mathematics

Use these symbols:

asked 2021-08-18

Discrete Mathematics Basics

1) Determine whether the relation R on the set of all Web pages is reflexive, symmetric, antisymmetric, and/or transitive, where$(a,b)\in R$ if and only if

I) everyone who has visited Web page a has also visited Web page b.

II) there are no common links found on both Web page a and Web page b.

III) there is at least one common link on Web page a and Web page b.

1) Determine whether the relation R on the set of all Web pages is reflexive, symmetric, antisymmetric, and/or transitive, where

I) everyone who has visited Web page a has also visited Web page b.

II) there are no common links found on both Web page a and Web page b.

III) there is at least one common link on Web page a and Web page b.

asked 2021-07-28

Let A, B, and C be sets. Show that

asked 2021-01-19

Let

Prove that

asked 2022-05-23

Exercise involving DFT

The fourier matrix is a transformation matrix where each component is defined as ${F}_{ab}={\omega}^{ab}$ where $\omega ={e}^{2\pi i/n}$. The indices of the matrix range from 0 to $n-1$ (i.e. $a,b\in \{0,...,n-1\}$)

As such we can write the Fourier transform of a complex vector v as $\hat{v}=Fv$, which means that

${\hat{v}}_{f}=\sum _{a\in \{0,...,n-1\}}{\omega}^{af}{v}_{a}$

Assume that n is a power of 2. I need to prove that for all odd $c\in \{0,...,n-1\}$, every $d\in \{0,...,n-1\}$ and every complex vectors v, if ${w}_{b}={v}_{cb+d}$, then for all $f\in \{0,...,n-1\}$ it is the case that:

${\hat{w}}_{cf}={\omega}^{-fd}\phantom{a}{\hat{v}}_{f}$

I was able to prove it for $n=2$ and $n=4$, so I tried an inductive approach. This doesn't seem to be the best way to go and I am stuck at the inductive step and I don't think I can go any further which indicates that this isn't the right approach.

Note that I am not looking for a full solution, just looking for a hint.

The fourier matrix is a transformation matrix where each component is defined as ${F}_{ab}={\omega}^{ab}$ where $\omega ={e}^{2\pi i/n}$. The indices of the matrix range from 0 to $n-1$ (i.e. $a,b\in \{0,...,n-1\}$)

As such we can write the Fourier transform of a complex vector v as $\hat{v}=Fv$, which means that

${\hat{v}}_{f}=\sum _{a\in \{0,...,n-1\}}{\omega}^{af}{v}_{a}$

Assume that n is a power of 2. I need to prove that for all odd $c\in \{0,...,n-1\}$, every $d\in \{0,...,n-1\}$ and every complex vectors v, if ${w}_{b}={v}_{cb+d}$, then for all $f\in \{0,...,n-1\}$ it is the case that:

${\hat{w}}_{cf}={\omega}^{-fd}\phantom{a}{\hat{v}}_{f}$

I was able to prove it for $n=2$ and $n=4$, so I tried an inductive approach. This doesn't seem to be the best way to go and I am stuck at the inductive step and I don't think I can go any further which indicates that this isn't the right approach.

Note that I am not looking for a full solution, just looking for a hint.

asked 2021-08-18

What if the centipede wants 50 (possibly different) matching pairs, one pair for each pair of feet? Consider first a centipede who only owns green and brown socks, then a centipede who also ownsstripey socks, and then a centipede who owns k different colors of socks.