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Brut [27]
3 years ago
15

For A = {a, b, c, d} fin P(A), the power set of A. (Compare to example 0.3.3 0n p22) For A- (a, b, c, d) find P(A), the power se

t of A.
Mathematics
1 answer:
Anna [14]3 years ago
7 0

Answer: The required set is {∅, {a},{b},{c},{d},{a,b},{a,c},{b,c}{c,d},{b,d},{d,a},{a,b,c},{b,c,d},{a,c,d},{a,b,d},{a,b,c,d}}

Step-by-step explanation:

Since we have given that

A= { a,b,c,d}

So, n = 4

We need to find the power set of A.

Number of elements in power set of A is 2^n=2^4=16

So, the power set of A has 16 elements.

So, P(A) becomes {∅, {a},{b},{c},{d},{a,b},{a,c},{b,c}{c,d},{b,d},{d,a},{a,b,c},{b,c,d},{a,c,d},{a,b,d},{a,b,c,d}}

Hence, the required set is {∅, {a},{b},{c},{d},{a,b},{a,c},{b,c}{c,d},{b,d},{d,a},{a,b,c},{b,c,d},{a,c,d},{a,b,d},{a,b,c,d}}

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On a certain hot​ summer's day, 391 people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for
Tomtit [17]

127 children and 264 adults swam at the public pool that day

Step-by-step explanation:

On a certain hot​ summer's day

  • 391 people used the public swimming pool
  • The daily prices are $1.25 for children and $2.25 for adults
  • The receipts for admission totaled $752.75

We need to find how many children and how many adults swam at the public pool that​ day

Assume that the number of children is x and the number of adult is y in that day

∵ x children swam that day

∵ y adults swam that day

∵ 391 people used the swimming pool that day

- Add x and y, then equate the sum by 391

∴ x + y = 391 ⇒ (1)

∵ The daily price for children is $1.25 per child

∵ The daily price for an adult is $2.25

∵ The receipts for admission totaled $752.75

- Multiply x by 1.25 and y by 2.25, then add the products and

  equate the sum by 752.75

∴ 1.25x + 2.25y = 752.75

- Divide each term by 1.25 to simplify the equation

∴ x + 1.8y = 602.2 ⇒ (2)

Now we have a system of equations to solve it

Subtract equation (1) from equation (2) to eliminate x

∵ (x - x) + (1.8y - y) = 602.2 - 391

∴ 0.8y = 211.2

- Divide both sides by 0.8

∴ y = 264

- Substitute the value of y in equation (1) to find x

∵ x + 264 = 391

- Subtract 264 from both sides

∴ x = 127

127 children and 264 adults swam at the public pool that day

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

#LearnwithBrainly

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Step-by-step explanation:

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