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Sergeeva-Olga [200]
3 years ago
6

Which is true. A B C D

Mathematics
2 answers:
Talja [164]3 years ago
8 0
The answer is B
It should be correct
gtnhenbr [62]3 years ago
7 0

Answer:

b

Step-by-step explanation:

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Determine,in each of the following cases, whether the described system is or not a group. Explain your answers. Determine what i
zheka24 [161]

Answer:

(a) Not a group

(b) Not a group

(c) Abelian group

Step-by-step explanation:

<em>In order for a system <G,*> to be a group, the following must be satisfied </em>

<em> (1) The binary operation is associative, i.e., (a*b)*c = a*(b*c) for all a,b,c in G </em>

<em>(2) There is an identity element, i.e., there is an element e such that a*e = e*a = a for all a in G </em>

<em> (3) For each a in G, there is an inverse, i.e, another element a' in G such that a*a' = a'*a = e (the identity) </em>

<em> </em>

If in addition the operation * is commutative (a*b = b*a for every a,b in G), then the group is said to be Abelian

(a)  

The system <G,*> is not a group since there are no identity.  

To see this, suppose there is an element e such that  

a*e = a

then  

a-e = a which implies e=0

It is easy to see that 0 cannot be an identity.

For example  

2*0 = 2-0 = 2

Whereas

0*2 = 0-2 = -2

So 2*0 is not equal to 0*2

(b)

The system <G,*> is not a group either.

If A is a matrix 2x2 and the determinant of A det(A)=0, then the inverse of A does not exist.

(c)

The table of the operation G is showed in the attachment.

It is evident that this system is isomorphic under the identity map, to the cyclic group

\mathbb{Z}_{5}

the system formed by the subset of Z, {0,1,2,3,4} with the operation of addition module 5, which is an Abelian cyclic group

We conclude that the system <G,*> is Abelian.

Attachment: Table for the operation * in (c)

4 0
3 years ago
Ronald and Tim did their laundry today. Ronald does laundry every 6 days and Tom does laundry every 9 days. How many days will i
Luden [163]
Least common multiple question

Ronald: count by 6's
 6, 12, 18, 24, 30, 36, 42, 48, 54 ....

Tim: count by 9's
9, 18, 27, 36, 45, 54,

every 18 days they do their laundry together
7 0
3 years ago
Given sin x = .24, find cos x
Nikolay [14]

Answer:

17?

Step-by-step explanation:

if i did it correctly it should be around that <3

4 0
3 years ago
Gabriel purchases a rug priced at $475. With sales tax, the total comes out to $513. What is the sales tax percentage?
Degger [83]

Answer:

The tax is 8%

Step-by-step explanation:

Take the final price and subtract the original price

513-475 = 38

Divide by the original price

38/475 =.08

Change to percent form

8%

The tax is 8%

8 0
2 years ago
Read 2 more answers
Mr. Smith is paid $9.50 per hour for fixing watches. Write an expression for the amount of money Mr. Smith earns in h hours. In
storchak [24]
9.50 + (2.20)r

For example if he fixed 3 watches

9.50 + (2.20)3

We plug in 3 for r and he makes 6.60 extra.
8 0
3 years ago
Read 2 more answers
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