Question

Let Z5={0,1,2,3,4}. Then, Z5 is Select one:

a. a group under subtraction

b. a group under addition modulo 5

c. a group under multiplication modulo 5

d. not a group under any operation

CLEAR MY CHOICE

Question 7

Not yet answered​

Answer 1

Answer:

b) one okkkkkkk it is correct

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

$\sf{Let \: \: Z_5 = \{ \bar{0},\bar{1},\bar{2},\bar{3},\bar{4} \} \: . Then \: Z_5 \: is}$

a. A group under subtraction

b. A group under addition modulo 5

c. A group under multiplication modulo 5

d. not a group under any operation

EVALUATION

Here the given set is

$\sf{Z_5 = \{ \bar{0},\bar{1},\bar{2},\bar{3},\bar{4} \} }$

Then

(i) the set is closed under addition

(ii) + is associative

(iii) $\sf{ \bar{0}}$ is the identity element

(iv)

$\sf{The \: inverse \: of \: \bar{0} \: \: is \: \bar{0}}$

$\sf{The \: inverse \: of \: \bar{1} \: \: is \: \bar{4}}$

$\sf{The \: inverse \: of \: \bar{2} \: \: is \: \bar{3}}$

$\sf{The \: inverse \: of \: \bar{3} \: \: is \: \bar{2}}$

$\sf{The \: inverse \: of \: \bar{4} \: \: is \: \bar{1}}$

Therefore the inverse of each element belongs to the set

So it forms a group under addition modulo 5

More over it is a abelian group

FINAL ANSWER

Hence the correct option is

b. A group under addition modulo 5

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