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Delvig [45]
3 years ago
11

Suppose H,K C G are subgroups of orders 5 and 8, respectively. Prove that H K = {e}.

Mathematics
1 answer:
kow [346]3 years ago
3 0

Step-by-step explanation:

Consider the provided information.

We have given that H and k are the subgroups of orders 5 and 8, respectively.

We need to prove that H∩K = {e}.

As we know "Order of element divides order of group"

Here, the order of each element of H must divide 5 and every group has 1 identity element of order 1.

1 and 5 are the possible order of 5 order subgroup.

For subgroup order 8: The possible orders are 1, 2, 4 and 8.

Now we want to find the intersection of these two subgroups.

Clearly both subgroup H and k has only identity element in common.

Thus, H∩K = {e}.

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Answer:

Bill suffered a loss of 42.85%.

Step-by-step explanation:

Bill bought a home for $210000 and sold it for $120000 and we have to calculate the percentage loss he suffered.

As we know loss suffered = Difference of sale price and cost price of the home.

Total loss = 210000-120000 = $90000

Now percentage loss = \frac{Total Loss }{cost price}.(100) = \frac{9000}{210000}.(100)

= 9/21×100 = 3×100/7 = 42.85%

So the answer is 42.85% loss.


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3 years ago
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Answer:

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Step-by-step explanation:

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Critical points are

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(positive)(positive) / (negative) = negative

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