Let P be the relation defined on the set of all American citizens by xPy if and only if x and y are registered for the same political party. Not being registered or being registered as an independent also counts as a registration. Check all properties that P has.anti-symmetric
reflexive
transitive
symmetric
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Answer:
This relation is symmetric, reflexive and transitive, but not anti-symmetric. Therefore it is an equivalence relation.
Step-by-step explanation:
Let's first prove that it is reflexive:
The explanation is as follows: let x be some american citizen, means that this person x is registered for the same political party as himself. This is obviously truth, because we are talking about the same person.
Next comes symmetry:
What does this statement mean? It means that if a is in the same party as b, then b is in the same party as a, and viceversa. This must be true, for the statement tells us that x is in the same party as y, which can also be stated as "x and y are both in the same party". This last statement also implies that y is in the same party as x, which is written as:
. That proves that:
And the converse follows from the same reasoning.
Now for Transitivity:
What this statement means in this context is that if a,b and c are american citizens, and we have that it is simultaneously true that both a and b are in the same party, and that also b and c are in the same party, then a and c must be also in the same party. This is true because parties are exclusive organisations, you cannot be both a democrat and a republican at the same time, or an independent and a republican. Therefore if a and b belong to the same party, and b and c also belong to the same party, it must be true that a belongs to the same party as b, and the same holds for c, therefore a and c belong to the same party (b's party). which we write as: . Thus it is true that R is a transitive relation.
Finally, Antisymmetry is NOT a property of this relation.
Let's see why, antisymmetry means:
That would mean that if x and y are two distinct american citizens , then if x is in the same party as y (
), then it is not true that y is in the same party as x! (
)
Clearly this isn't true, for example if x and y are two distinct democratic party members, we can say that that is, x and y are registered for the same party, and given that this relation is symmetric, as we have shown, we can also say
, but this comes in conflict with the definition of antisymmetry. Thus we conclude that the relation R is not antisymmetric.
On a final note, it's interesting to point out that reflexivity, symmetry and transitivity are the requirements for a relation to be an equivalence relation, which is a very useful concept in maths.
Final answer:
The relation P defined on the set of all American citizens by xPy is reflexive and symmetric, but not transitive.
Explanation:
The relation P defined on the set of all American citizens by xPy if and only if x and y are registered for the same political party has the properties of reflexivity, symmetry, but not transitivity.
Reflexivity means that every element is related to itself. In this case, every American citizen is registered for the same political party as themselves, including those who are registered as independent or not registered at all.
Symmetry means that if x is related to y, then y is related to x. In this case, if two American citizens are registered for the same political party, they are related to each other.
However, the relation P does not have the property of transitivity. Transitivity means that if x is related to y and y is related to z, then x is related to z. In the case of the relation P, if two American citizens are registered for the same political party and another two American citizens are registered for the same political party, it is not necessarily true that the first two citizens are also registered for the same political party as the second two citizens.
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Does anyone wanna help
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= 4k^4 + 2 - 3k + 5k^4 + k - 8
= 9k^4 -2k -6
The simplest form is 9k^4 -2k -6
You can only add values that have the same terms
4k^4 + 5k^4 = 9k^4
-3k + k = -2k
-8 + 2 = -6
The answer is 9k^4 - 2k - 6
Hope this helps!
Which of these sentences is always true for a parallelogram?
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Letter D
Remember to drink water
Answer:
parallelograms are shapes that have 2 sets of parallel sides. for example, squares, rectangles, and rhombuses are all types of parallelograms
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Answer:
8 3 + 4 2 + 7 − 7
Step-by-step explanation:
Distribute
(103+72−7)−1(23+32−7)
(103+72−7)−23−32+7
Eliminate redundant parentheses
(103+72−7)−23−32+7
103+72−7−23−32+7
Combine like terms
103+72−7−23−32+7
83+72−7−32+7
Combine like terms
83+72−7−32+7
83+42−7+7
Rearrange terms
83+42−7+7
83+42+7−7
Answer:
-8x3 - 4x2-7x + 7
Step-by-step explanation:
Answers
Answer:
1) Fail to reject the Null hypothesis
2) We do not have sufficient evidence to support the claim that the mean distance students traveled to school from their current residence was different for males and females.
Step-by-step explanation:
A university administrator wants to test if there is a difference between the distance men and women travel to class from their current residence. So, the hypothesis would be:
The results of his tests are:
t-value = -1.05
p-value = 0.305
Degrees of freedom = df = 21
Based on this data we need to draw a conclusion about test. The significance level is not given, but the normally used levels of significance are 0.001, 0.005, 0.01 and 0.05
The rule of the thumb is:
- If p-value is equal to or less than the significance level, then we reject the null hypothesis
- If p-value is greater than the significance level, we fail to reject the null hypothesis.
No matter which significance level is used from the above mentioned significance levels, p-value will always be larger than it. Therefore, we fail to reject the null hypothesis.
Conclusion:
We do not have sufficient evidence to support the claim that the mean distance students traveled to school from their current residence was different for males and females.
Final answer:
The Minitab output from the t-test signifies that there is no statistically significant difference in the distances traveled by men and women at UF to get to class. The t-value and p-value obtained don't give enough evidence to reject the null hypothesis. The degrees of freedom (DF) indicate the number of independent observations in the sample.
Explanation:
The output from Minitab that you've shared is the result of a paired t-test comparing the mean distances traveled by men and women to get to class at UF. The null hypothesis in this context is that there is no difference in the average distances traveled by men and women (Difference = mu (F) - mu (M)). The t-value of -1.05 and the p-value of 0.305 do not provide enough evidence to reject the null hypothesis at the conventional 0.05 level of significance. Therefore, we could interpret the output as not detecting a statistically significant difference between the mean distances men and women travel to get to class at UF.
The 'DF' or degrees of freedom, indicates the number of independent observations in your sample that are free to vary once certain constraints (like the sample mean) are calculated. In this case, DF = 21, which is the sample size (pairs of men and women) minus 1.
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