PoentWeptgj
2022-07-15
Answered

The board of directors of a pharmaceutical corporation has 10 members. Three members of the board of directors are physicians. How many different slates consisting of a president, vice president, secretary, and treasurer be made with exactly one physician. Note that there are 3 physicians out of the 10 directors.

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asked 2020-11-09

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

asked 2021-08-18

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 2021-08-02

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 2021-07-28

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

asked 2022-09-05

Information about this type of recurrence relation

I've been noodling with a problem that requires me to find a set of recurrence relations and their solutions. In particular, all the recurrence relations are of the form:

$${u}_{n+1}={u}_{n}+p(n)$$

where p(x) is a polynomial.

I've been noodling with a problem that requires me to find a set of recurrence relations and their solutions. In particular, all the recurrence relations are of the form:

$${u}_{n+1}={u}_{n}+p(n)$$

where p(x) is a polynomial.

asked 2022-09-05

Simplification of expression (related to multinomial theorem)

Is there a simplified way to write the following:

$$\sum _{{r}_{1}+{r}_{2}+\cdots +{r}_{n}=t,{r}_{k}\in \mathbb{N}}\frac{t!}{{r}_{1}!{r}_{2}!\cdots {r}_{n}!}\prod _{k=1}^{n}f(k{)}^{{r}_{k}}$$

This is very similar to the multinomial theorem formula, however instead of ${r}_{k}$ being non-negative, ${r}_{k}$ is a natural number. In an expansion this is equivalent to just taking the values where every term is exponentiated to a power of one or greater, for example in the expansion of $(a+b+c{)}^{4}$ just taking $3(2{a}^{2}bc+2a{b}^{2}c+2ab{c}^{2})$.

Is there a simplified way to write the following:

$$\sum _{{r}_{1}+{r}_{2}+\cdots +{r}_{n}=t,{r}_{k}\in \mathbb{N}}\frac{t!}{{r}_{1}!{r}_{2}!\cdots {r}_{n}!}\prod _{k=1}^{n}f(k{)}^{{r}_{k}}$$

This is very similar to the multinomial theorem formula, however instead of ${r}_{k}$ being non-negative, ${r}_{k}$ is a natural number. In an expansion this is equivalent to just taking the values where every term is exponentiated to a power of one or greater, for example in the expansion of $(a+b+c{)}^{4}$ just taking $3(2{a}^{2}bc+2a{b}^{2}c+2ab{c}^{2})$.

asked 2021-07-20

Select the correct general solution for the recurrence relation given below: