Question

6. Find the values for each of the following: a. 3 times 5 in Z1o b. 3 times 5 in Zs c. 3 times 5 in Z3 e. 5 3 in Z1o

Answer 1

Answer: The calculations are done below.

Step-by-step explanation: We are given to find the values for each of the following :

(A) 3 times 5 in
`\mathbb{Z}_(10).`

We know that

`\mathbb{Z}_(10)=\{0,1,2,3,4,5,6,7,8,9\}(\textup{mod}10).`

Therefore, we get

`3*5=15(\textup{mod}10)=5.`

(B) 3 times 5 in
`\mathbb{Z}_(5).`

We know that

`\mathbb{Z}_(5)=\{0,1,2,3,4\}(\textup{mod}5).`

Therefore, we get

`3*5=15(\textup{mod}5)=0.`

(C) 3 times 5 in
`\mathbb{Z}_(3).`

We know that

`\mathbb{Z}_(3)=\{0,1,2\}(\textup{mod}3).`

Therefore, we get

`3*5=15(\textup{mod}3)=0.`

(D) 5 times 3 in
`\mathbb{Z}_(10).`

We know that

`\mathbb{Z}_(10)=\{0,1,2,3,4,5,6,7,8,9\}(\textup{mod}10).`

Therefore, we get

`5*3=15(\textup{mod}10)=5.`

Thus, the required values are evaluated.