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klemol [59]
3 years ago
13

Suppose R is a symmetric and transitive relation on a set A, and there is an element a in A for which aRx for every x in A. Prov

e that R is reflexive. ...?
Mathematics
1 answer:
topjm [15]3 years ago
7 0
According to what I have researched, here is how you prove that R is reflexive.
let b∈A
then, aRb
and by symmetry, bRa
and by transitivity,<span><span>bRa,aRb⇒bRb
Hope this is the answer that you are looking for. 
Thank you for posting your question here in brainly.</span></span>
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What is 2 2/5×2 7/9 in simplest mixed number form?
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6 2/3

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2 2/5 * 2 7/9

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3 years ago
Tain has a great literary tradition that spans centuries. One might assume, then, that Britons read more than citizens of other
tresset_1 [31]

Answer:

Null hypothesis:p_{1} \leq p_{2}  

Alternative hypothesis:p_{1} > p_{2}  

z=3.02  

p_v =P(Z>3.02)=0.00127  

The p value is a very low value and using any significance level for example \alpha=0.05, 0,1,0.15 always p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion of Canadians is not significantly higher than the porportions of readers at Britons.  

Step-by-step explanation:

1) Data given and notation  

X_{1}=0.86*1004 represent the number of Canadians randomly sampled by Gallup that read at least one book in the past year

X_{2}=0.81*1009 represent the number of Britons randomly sampled that read at least one book in the past year

n_{1}=1004 sample of Gallup selected

n_{2}=1009 sample of Britons selected

p_{1}=0.86 represent the proportion of Canadians randomly sampled by Gallup that read at least one book in the past year

p_{2}=0.81 represent the proportion of Britons randomly sampled that read at least one book in the past year

z would represent the statistic (variable of interest)  

p_v represent the value for the test (variable of interest)

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the proportion for men with red/green color blindness is a higher than the rate for women  , the system of hypothesis would be:  

Null hypothesis:p_{1} \leq p_{2}  

Alternative hypothesis:p_{1} > p_{2}  

We need to apply a z test to compare proportions, and the statistic is given by:  

z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}   (1)

Where \hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{0.81+0.86}{2}=0.835

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:  

z=\frac{0.86-0.81}{\sqrt{0.835(1-0.835)(\frac{1}{1004}+\frac{1}{1009})}}=3.02  

4) Statistical decision

For this case we don't have a significance level provided \alpha, but we can calculate the p value for this test.  

Since is a one side test the p value would be:  

p_v =P(Z>3.02)=0.00127  

So the p value is a very low value and using any significance level for example \alpha=0.05, 0,1,0.15 always p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion of Canadians is not significantly higher than the porportions of readers at Britons.  

5 0
3 years ago
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