Question

how many elements in z6 is​

Answer 1

Answer:

Step-by-step explanation:

Given,

Answer 2

Answer:

The number of the elements in $Z_6$ are 6.

Step-by-step explanation:

Concept:-

• $Z_6$ is the integers modulo 6.
• In general, the integers mod n is the set $Z_n = \{0,1,2,.\ .\ .,n-1\}$. n is called the modulus.
• $Z_6$ is cyclic as well as abelian group (All cyclic groups are abelian).
• The units in $Z_6$ are 1 and 5.
• And the subgroups of $Z_6$ are $\{0\}$, $\{3\}$ and $\{2\}$.
• The order of the group $Z_6$ is 6.

According to the question,

Given:-

The group $Z_6$.

To find:-

The number elements in $Z_6$ group.

Since the elements of the set $Z_n$ are $\{0,1,2,.\ .\ .,n-1\}$, i.e.,

$Z_n = \{0,1,2,.\ .\ .,n-1\}$

Substitute the value 6 for n as follows:

$Z_6 = \{0,1,2,.\ .\ .,6-1\}$

$Z_6 = \{0,1,2,3,4,5\}$

Clearly, $Z_6$ contains 6 elements.

Final answer: The number of the elements in $Z_6$ are 6.

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