Question

Let us assign numeric value to the uppercase alphabet (A=0, B=1, …, Z=25). We can now do modular arithmetic on the system using modulo 26.

(a). What is (A+N) mod (26) in this system:
(b). What is (A+6) mod (26) in this system:
(c). What is (Y-5) mod (26) in this system:
(d). What is (C-10) mod (26) in this system:

Answer 1

In this modular arithmetic system, (A+N) mod (26) simplifies to the remainder of N divided by 26. For example, (A+10) mod (26) will be 10. Applying the same concept, (A+6) mod (26) is 6, (Y-5) mod (26) is 19, and (C-10) mod (26) is 18.

Step-by-step explanation:

In this modular arithmetic system, with A=0 and Z=25, we do calculations using modulo 26. This means that (A+N) mod (26) can be simplified to (0+N) mod (26) as A=0. So, the result of (A+N) mod (26) will be the remainder when N is divided by 26. For example, if N=10, then (A+N) mod (26) = (0+10) mod (26) = 10.

Using the same concept, (A+6) mod (26) can be simplified to (0+6) mod (26), which is equal to 6. So, the answer is 6.

Similarly, (Y-5) mod (26) can be simplified to (24-5) mod (26), which is equal to 19. So, the answer is 19.

And (C-10) mod (26) can be simplified to (2-10) mod (26), which is equal to 18. So, the answer is 18.