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Mama L [17]
3 years ago
8

Suppose that X is a subset of Y. Let p be the proposition ‘x is an element ofX’ and let q be the proposition ‘x is an element of

Y’. Write down apropositional term which represents the statement ‘x is an element ofY \X ’. Hence or otherwise, establish the following identities for sets:(i) A n B = A\Bc;(ii) A U (B\A) = A U B;(iii) A\(B U C) = (A\B) n (A\C);(iv) A\(B n C) = (A\B) U (A\C).
Mathematics
1 answer:
Genrish500 [490]3 years ago
8 0

Answer:

See answer below

Step-by-step explanation:

The statement ‘x is an element of Y \X’ means, by definition of set difference, that "x is and element of Y and x is not an element of X", WIth the propositions given, we can rewrite this as "p∧¬q". Let us prove the identities given using the definitions of intersection, union, difference and complement. We will prove them by showing that the sets in both sides of the equation have the same elements.

i) x∈AnB  if and only (if and only if means that both implications hold) x∈A and x∈B if and only if x∈A and x∉B^c (because B^c is the set of all elements that do not belong to X) if and only if x∈A\B^c. Then, if x∈AnB  then x∈A\B^c, and if x∈A\B^c then x∈AnB. Thus both sets are equal.

ii) (I will abbreviate "if and only if" as "iff")

x∈A∪(B\A) iff x∈A or x∈B\A iff x∈A or x∈B and x∉A iff x∈A or x∈B (this is because if x∈B and x∈A then x∈A, so no elements are lost when we forget about the condition x∉A) iff x∈A∪B.

iii) x∈A\(B U C) iff x∈A and x∉B∪C iff x∈A and x∉B and x∉C (if x∈B or x∈C then x∈B∪C thus we cannot have any of those two options). iff x∈A and x∉B and x∈A and x∉C iff x∈(A\B) and x∈(A\B) iff x∈ (A\B) n (A\C).

iv) x∈A\(B ∩ C) iff x∈A and x∉B∩C iff x∈A and x∉B or x∉C (if x∈B and x∈C then x∈B∩C thus one of these two must be false) iff x∈A and x∉B or x∈A and x∉C iff x∈(A\B) or x∈(A\B) iff x∈ (A\B) ∪ (A\C).

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There were 27,000 people at a ball game in Los Angeles. The day's receipts were $204,000. How many people paid $13 for reserved
Studentka2010 [4]
21000 people paid for general admission and 6000 paid for reserved seats. This is solved by making 2 equations. Out of 27000 people who were at game, x of them paid for general admission and y for reserved seats, thus
x + y = 27000
As said, daily receipts were 204000$. As reserved seat is 13$, y of them gave 13$ each (y*13$) and x of them gave 6 for general admission(x*6) and those two add up and we get second equation
13y + 6x = 204000.
This can be solved by transforming first equation into x = 27000 - y and then replacing the x in second.
13y + 6*(27000 - y) = 204000
13y + 162000 - 6y = 204000
7y = 42000
y = 6000
x + 6000 = 27000
x = 27000 - 6000 = 21000
5 0
3 years ago
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 421 gram setting. It is
Anastaziya [24]

Answer:

The p-value is approximately 0.0508

Step-by-step explanation:

The given parameters are;

The expected mass of banana chips bag filled by the machine, μ = 421 gams

The number of bags in the sample of bags filled by the machine, n = 26 bags

The mean mass of the bags in the sample, \overline x = 413 grams

The standard deviation of the mass in the bags, s = 24 grams

The level of significance, α = 0.02

The null hypothesis, H₀; μ = 421 grams

The alternative hypothesis, Hₐ; μ < 421 grams

The test statistic is given as follows;

t=\dfrac{\bar{x}-\mu }{\dfrac{s}{\sqrt{n}}}

We get;

t=\dfrac{413-421 }{\dfrac{24}{\sqrt{26}}} \approx -1.6996731712

The t-value = -1.6996731712

The degrees of freedom df = n - 1 = 26 - 1 = 25

From an online source, we get the critical-t =  2.166587

The p-value is obtained using an online source as p(t ≤  -1.6996731712) = 0.0508

From the p-value table, we get

0.05 < p < 0.1

3 0
2 years ago
An automobile factory,1849 parts are made in 4 hours.what is the average rate at which parts are made per hour?
MAXImum [283]

Answer:

There are 462.25 parts being made per hour

Step-by-step explanation:

<u>Step 1:  Make an equation</u>

An automobile factory, 1849 parts are made in 4 hours.

<em>1849 / 4 = x</em>

<em />

<u>Step 2:  Solve</u>

1849 / 4 = x

<em>462.25 = x</em>

<em />

Answer:  There are 462.25 parts being made per hour

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150 is smaller than 200 so 25 is smaller than 40, but 25, in perspective to the numbers, is much smaller than 40. Ana is faster.

Check:

Takashi: 200 divided by 400 equals 5 yd/sec
Ana: 150 divided by 25 equals 6 yd/sec
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Ber [7]

Answer:

The answer is either a or c .

Step-by-step explanation:

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