enmobladatn
2022-07-15
Answered

Negate the statement and express your answer in a smooth english sentence. Hint first rewrite the statement so that it does not contain an implication. The statement is: If the bus is not coming, then I cannot get to school.

You can still ask an expert for help

Selden1f

Answered 2022-07-16
Author has **14** answers

Step 1

The negation of:

$\mathrm{\neg}p\to \mathrm{\neg}q$

is:

$\mathrm{\neg}p\wedge q$

Step 2

Answer:

"The bus is not coming and I can get to school".

The negation of:

$\mathrm{\neg}p\to \mathrm{\neg}q$

is:

$\mathrm{\neg}p\wedge q$

Step 2

Answer:

"The bus is not coming and I can get to school".

Darian Hubbard

Answered 2022-07-17
Author has **7** answers

Step 1

Here is what you should do in logic:

$\begin{array}{rl}& \mathrm{\neg}\left(P\to R\right)\leftrightarrow \mathrm{\neg}\left(\mathrm{\neg}P\vee R\right)\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}Conditional\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}Disjunction\\ & \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\text{}\leftrightarrow \mathrm{\neg}\mathrm{\neg}P\wedge \mathrm{\neg}R\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}Demorga{n}^{\prime}s\phantom{\rule{thinmathspace}{0ex}}Law\\ & \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\text{}\leftrightarrow \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}P\wedge \mathrm{\neg}R\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}Double\phantom{\rule{thinmathspace}{0ex}}Negation\end{array}$

Step 2

your P and Q are

$P=$ the bus is not coming

$Q=I$ cannot get to school

so the negation is:

the bus is not coming and I can get to school

Here is what you should do in logic:

$\begin{array}{rl}& \mathrm{\neg}\left(P\to R\right)\leftrightarrow \mathrm{\neg}\left(\mathrm{\neg}P\vee R\right)\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}Conditional\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}Disjunction\\ & \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\text{}\leftrightarrow \mathrm{\neg}\mathrm{\neg}P\wedge \mathrm{\neg}R\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}Demorga{n}^{\prime}s\phantom{\rule{thinmathspace}{0ex}}Law\\ & \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\text{}\leftrightarrow \phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}P\wedge \mathrm{\neg}R\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}Double\phantom{\rule{thinmathspace}{0ex}}Negation\end{array}$

Step 2

your P and Q are

$P=$ the bus is not coming

$Q=I$ cannot get to school

so the negation is:

the bus is not coming and I can get to school

asked 2021-08-15

How many elements are in the set
{ 0, { { 0 } }?

asked 2021-07-28

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

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) Find out if the relation R is transitive, symmetric, antisymmetric, or reflexive on the set of all web pages.where $(a,b)\in R$ if and only if

I)Web page a has been accessed by everyone who has also accessed Web page b.

II) Both Web page a and Web page b lack any shared links.

III) Web pages a and b both have at least one shared link.

asked 2022-09-06

Trying to solve a simple-looking recurrence relation

I have this recurrence relation that I've been trying to solve,

$${g}_{m}={g}_{m-1}+{a}_{m}\phantom{\rule{thinmathspace}{0ex}}{g}_{m-2}$$

with ${g}_{1}={g}_{0}=1$ and $m\ge 0$. Here, ${a}_{m}$ is the m-th term of a known sequence. Any ideas?

If it helps, ${a}_{m}=\frac{1}{{L}^{2}}(m-1)(r-m+2)$ where ${L}^{2}\in \mathbb{Z},{L}^{2}\ne 0$, $r\in {\mathbb{N}}_{0}$ and $r\ge |L|$, but other than that, L and r are free. So, if I were to be extremely precise, ${g}_{m}$ and ${a}_{m}$ would actually be ${g}_{mrL}$ and ${a}_{mrL}$.

I have this recurrence relation that I've been trying to solve,

$${g}_{m}={g}_{m-1}+{a}_{m}\phantom{\rule{thinmathspace}{0ex}}{g}_{m-2}$$

with ${g}_{1}={g}_{0}=1$ and $m\ge 0$. Here, ${a}_{m}$ is the m-th term of a known sequence. Any ideas?

If it helps, ${a}_{m}=\frac{1}{{L}^{2}}(m-1)(r-m+2)$ where ${L}^{2}\in \mathbb{Z},{L}^{2}\ne 0$, $r\in {\mathbb{N}}_{0}$ and $r\ge |L|$, but other than that, L and r are free. So, if I were to be extremely precise, ${g}_{m}$ and ${a}_{m}$ would actually be ${g}_{mrL}$ and ${a}_{mrL}$.

asked 2022-09-04

Help with Strong Induction proof

$${A}_{n}=\{\begin{array}{ll}3,& n=1\\ 9,& n=2\\ 2{A}_{n-1},& n\ne 1\text{and}n\text{odd}\\ 4{A}_{n-1},& n\text{even}\end{array}$$

Need to prove ${A}_{n}\le {3}^{n}$ $\forall n$ in $N\ge 1$ by strong induction. After case $n=1$ and $n=2$, i thought about going for something like $n=2k$ for n even and $n=2k+1$ for n odd but i got stuck and have yet no idea how to proceed after the two inicial cases.

$${A}_{n}=\{\begin{array}{ll}3,& n=1\\ 9,& n=2\\ 2{A}_{n-1},& n\ne 1\text{and}n\text{odd}\\ 4{A}_{n-1},& n\text{even}\end{array}$$

Need to prove ${A}_{n}\le {3}^{n}$ $\forall n$ in $N\ge 1$ by strong induction. After case $n=1$ and $n=2$, i thought about going for something like $n=2k$ for n even and $n=2k+1$ for n odd but i got stuck and have yet no idea how to proceed after the two inicial cases.

asked 2021-08-20

Determine whether the following set equivalence is true

$(A\cup B)\text{}(A\cap C)=B\cup \left(A\text{}C\right)$