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

$3\times5=15(\textup{mod}10)=5.$

(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

$3\times5=15(\textup{mod}5)=0.$

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

We know that

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

Therefore, we get

$3\times5=15(\textup{mod}3)=0.$

(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

$5\times3=15(\textup{mod}10)=5.$

Thus, the required values are evaluated.