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Anon25 [30]
2 years ago
15

Doughnuts cost $3.45 for a dozen at Store A, and cost $2.40 for 8

Mathematics
1 answer:
GalinKa [24]2 years ago
5 0

Answer:

store A is cheaper

Step-by-step explanation:

All right. If you divide Store A's numbers like so,

3.45 / 12, you'd get about 0.28, which is the average cost per one donut at store A.

For store B, if you divided,

2.40/8, you'd get 0.30, which is the average cost per one donut at store B, which means that store A is cheaper!

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Let A, B, C and D be sets. Prove that A \ B and C \ D are disjoint if and only if A ∩ C ⊆ B ∪ D
ANEK [815]

Step-by-step explanation:

We have to prove both implications of the affirmation.

1) Let's assume that A \ B and C \ D are disjoint, we have to prove that A ∩ C ⊆ B ∪ D.

We'll prove it by reducing to absurd.

Let's suppose that A ∩ C ⊄ B ∪ D. That means that there is an element x that belongs to A ∩ C but not to B ∪ D.

As x belongs to A ∩ C, x ∈ A and x ∈ C.

As x doesn't belong to B ∪ D, x ∉ B and x ∉ D.

With this, we can say that x ∈ A \ B and x ∈ C \ D.

Therefore, x ∈ (A \ B) ∩ (C \ D), absurd!

It's absurd because we were assuming that A \ B and C \ D were disjoint, therefore their intersection must be empty.

The absurd came from assuming that A ∩ C ⊄ B ∪ D.

That proves that A ∩ C ⊆ B ∪ D.

2) Let's assume that A ∩ C ⊆ B ∪ D, we have to prove that A \ B and C \ D are disjoint (i.e.  A \ B ∩ C \ D is empty)

We'll prove it again by reducing to absurd.

Let's suppose that  A \ B ∩ C \ D is not empty. That means there is an element x that belongs to  A \ B ∩ C \ D. Therefore, x ∈ A \ B and x ∈ C \ D.

As x ∈ A \ B, x belongs to A but x doesn't belong to B.  

As x ∈ C \ D, x belongs to C but x doesn't belong to D.

With this, we can say that x ∈ A ∩ C and x ∉ B ∪ D.

So, there is an element that belongs to A ∩ C but not to B∪D, absurd!

It's absurd because we were assuming that A ∩ C ⊆ B ∪ D, therefore every element of A ∩ C must belong to B ∪ D.

The absurd came from assuming that A \ B ∩ C \ D is not empty.

That proves that A \ B ∩ C \ D is empty, i.e. A \ B and C \ D are disjoint.

7 0
3 years ago
I need to know what the answer is?<br>is it x,y,z,or w?​
andrew-mc [135]

Answer:

Y

Step-by-step explanation:

5 0
3 years ago
BRAINLIEST!! What’s 36.3 square root ?
Marat540 [252]

Answer:

6.02

Step-by-step explanation:

4 0
2 years ago
Please help me find the value of X!!!!!! Please!!!!
Luda [366]

Answer:

52

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
(<img src="https://tex.z-dn.net/?f=%28%5Csqrt%7B6%7D%20%2B%5Csqrt%7B3%7D%29%28%5Csqrt%7B2%7D-2%29" id="TexFormula1" title="(\sqr
Marta_Voda [28]

Answer:

-2.453

Step-by-step explanation:

sqrt(6) * sqrt(2) = 3.461

sqrt(6) * -2 = -4.899

sqrt(3) * sqrt(2) = 2.449

sqrt(3) * -2 = -3.464

sum of numbers equals

-2.453

7 0
3 years ago
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