True and False?

If $A$, $B$, and $C$ are three sets, then the only way that $A\cup C$ can equal $B\cup C$ is $A=B$.

If $A$, $B$, and $C$ are three sets, then the only way that $A\cup C$ can equal $B\cup C$ is $A=B$.

Jase Rocha
2022-09-23
Answered

True and False?

If $A$, $B$, and $C$ are three sets, then the only way that $A\cup C$ can equal $B\cup C$ is $A=B$.

If $A$, $B$, and $C$ are three sets, then the only way that $A\cup C$ can equal $B\cup C$ is $A=B$.

You can still ask an expert for help

Sarah Sutton

Answered 2022-09-24
Author has **4** answers

False, if $C\supseteq B,A$ then the hypothesis is trivial, but the conclusion is not.

asked 2022-06-22

A store-bought pregnancy test produces a correct result 99% of the time when a woman is actually pregnant but is only 97% accurate when a woman is not pregnant. What are the chances of a false positive and a false negative respectively?

So I have tried to solve it and is the false positive 3%? SO, false positive is when the result shows positive despite her not being pregnant. And for her not being pregnant , the test is 97% accurate. Then, the false positive should be 100-97%?

So I have tried to solve it and is the false positive 3%? SO, false positive is when the result shows positive despite her not being pregnant. And for her not being pregnant , the test is 97% accurate. Then, the false positive should be 100-97%?

asked 2022-08-26

The smallest positive integer in the set $\{6u+9v:u,v=\text{integers}\}$ is $1$.

My thoughts: false. there is no value of $u$ and $v$ (positive or negative) that could result in a remainder of $1$. Smallest positive I get is $3$. Solid foundation to prove it?

My thoughts: false. there is no value of $u$ and $v$ (positive or negative) that could result in a remainder of $1$. Smallest positive I get is $3$. Solid foundation to prove it?

asked 2022-06-08

if 1:1000 of people is sick. the probability to be false positive is 0.07. if a person is sick there is not chance the test for the disease is wrong. If someone random is got a positive result, what are the chances he's actually sick?

I got 1.5% and wanted to check because I feel it should be more since the diagnose is never wrong. I took 1/1000 and divided it by 0.07+1/1000 and multiplied by 100 to get the percent.

I got 1.5% and wanted to check because I feel it should be more since the diagnose is never wrong. I took 1/1000 and divided it by 0.07+1/1000 and multiplied by 100 to get the percent.

asked 2022-10-20

Let $X$ be a locally comapct and Hausdorff space. We say a positive Radon Measure on $X$ is faithful if

$$0\le f\text{}\text{}\text{},\text{}\text{}\text{}\int fd\mu =0\to f(x)=0\text{}\text{}\mathrm{\forall}x\in X$$

True or false: If there is a faithful positive Radon measure on $X$ then $X$ has a countable dense subset ?

$$0\le f\text{}\text{}\text{},\text{}\text{}\text{}\int fd\mu =0\to f(x)=0\text{}\text{}\mathrm{\forall}x\in X$$

True or false: If there is a faithful positive Radon measure on $X$ then $X$ has a countable dense subset ?

asked 2022-11-01

The occurrence of a disease is $\frac{1}{100}=P(D)$

The false negative probability is $\frac{6}{100}=P(-|D)$, and the false positive is $\frac{3}{100}=P(+|\mathrm{\neg}D)$

Compute $P(D|+)$

By bayes formula,

$P(+)=P(+|D)P(D)+P(+|\mathrm{\neg}D)P(\mathrm{\neg}D)=\frac{97}{10000}+\frac{297}{10000}=\frac{394}{10000}$

Similarly $P(D|+)=\frac{P(+|D)P(D)}{P(+)}=\frac{97}{394}=0.246$

Is this correct?

The false negative probability is $\frac{6}{100}=P(-|D)$, and the false positive is $\frac{3}{100}=P(+|\mathrm{\neg}D)$

Compute $P(D|+)$

By bayes formula,

$P(+)=P(+|D)P(D)+P(+|\mathrm{\neg}D)P(\mathrm{\neg}D)=\frac{97}{10000}+\frac{297}{10000}=\frac{394}{10000}$

Similarly $P(D|+)=\frac{P(+|D)P(D)}{P(+)}=\frac{97}{394}=0.246$

Is this correct?

asked 2022-06-10

5% of the population have the disease (D). A test is available that has a 10% false positive and a 10% false negative rate.

part (B) of the question asks what is the probability of having the disease given that you test positive. I'm quite confident the answer to this is ~ 32%

Part (D) - Suppose that there is no cost or benefit from testing negative but a benefit B from true positives which detect the disease and a cost C to false positives.

i) What is the expected value of the testing programme?

ii) What benefit-cost ratio would you require to proceed with the testing programme?

I'm not quite sure to how to answer either of part D. My somewhat educated guesses are

the expected value = 0.045B - 0.095C

and the benefit to cost ratio required to proceed with the testing programme is 2.11 (or greater)

part (B) of the question asks what is the probability of having the disease given that you test positive. I'm quite confident the answer to this is ~ 32%

Part (D) - Suppose that there is no cost or benefit from testing negative but a benefit B from true positives which detect the disease and a cost C to false positives.

i) What is the expected value of the testing programme?

ii) What benefit-cost ratio would you require to proceed with the testing programme?

I'm not quite sure to how to answer either of part D. My somewhat educated guesses are

the expected value = 0.045B - 0.095C

and the benefit to cost ratio required to proceed with the testing programme is 2.11 (or greater)

asked 2022-06-27

Could Miller-Rabin primality test give false negative, for example when test prime number and gives it as composite?