True and False?

If $(A\cup B\subset A\cup C)$ then $B\subset C$

If $(A\cup B\subset A\cup C)$ then $B\subset C$

Ciara Rose
2022-07-17
Answered

True and False?

If $(A\cup B\subset A\cup C)$ then $B\subset C$

If $(A\cup B\subset A\cup C)$ then $B\subset C$

You can still ask an expert for help

Helena Howard

Answered 2022-07-18
Author has **12** answers

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

asked 2022-11-09

"The population, for a disease D, has a true rate of T%"

"Some Test ST, has false positive rate of FP% and a false negative rate of FN%."

"T, FP, and FN are elements of the set of real numbers."

Was the number T determined by some 100% accurate and possibly expensive test?

"Some Test ST, has false positive rate of FP% and a false negative rate of FN%."

"T, FP, and FN are elements of the set of real numbers."

Was the number T determined by some 100% accurate and possibly expensive test?

asked 2022-06-06

For what composite numbers $x$ will ${a}^{x-1}\equiv 1\phantom{\rule{0.444em}{0ex}}(\mathrm{mod}\phantom{\rule{0.333em}{0ex}}x)$ for $a\in [2,n]$?

Can we generate $x$s that give false positives to the Rabin-Miller test for the first, say $10$, consecutive integers $a>1$?

Can we generate $x$s that give false positives to the Rabin-Miller test for the first, say $10$, consecutive integers $a>1$?

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 2022-11-09

While it makes some sense, it's not clear to me why those are different. If a test, say medical test, is correct 90% of time then chances of it being wrong is 10%.

There are 4 events

1. Test is +, patient has a disease

2. Test is -, patient doesn't have a disease

3. Test is +, patient doesn't have a disease

4. Test is -, patient has a disease

There are 4 events

1. Test is +, patient has a disease

2. Test is -, patient doesn't have a disease

3. Test is +, patient doesn't have a disease

4. Test is -, patient has a disease

asked 2022-05-10

in order to remember stuff i need to understand their reason. Right now i cannot remember what is type 1 error and what is type 2 error why is the reason type 1 is false positive?

asked 2022-04-07

A pregnancy test kit is 98.5% accurate for true positive result, i.e. the result is positive when the tester is actually pregnant. If she is not pregnant, however, it may yield a 0.8% false positive. Suppose a woman using this pregnancy kit is 60% at risk of being pregnant.

Not sure about her first test which turned out to be negative, the woman decides to take the test again. This second test, however, turns out to be positive. Assuming the two test are independent, find the probability that she is actually pregnant.

Now she is so confused whether or not she is pregnant. So she take the tests n more times and the results for these n more tests are all positive. Find the minimum value for n so that she can be at least 99.99% sure of pregnancy, assuming all test are independent.

Not sure about her first test which turned out to be negative, the woman decides to take the test again. This second test, however, turns out to be positive. Assuming the two test are independent, find the probability that she is actually pregnant.

Now she is so confused whether or not she is pregnant. So she take the tests n more times and the results for these n more tests are all positive. Find the minimum value for n so that she can be at least 99.99% sure of pregnancy, assuming all test are independent.

asked 2022-04-06

The occurrence of false positives [in some experiment] is 40%

What does this mean? Does it mean that 40% of positives are false? Or 40% of all tested patients are specifically both false and positive? Or say 40% of those that are false are positive?

What does this mean? Does it mean that 40% of positives are false? Or 40% of all tested patients are specifically both false and positive? Or say 40% of those that are false are positive?