Here are the solutions to the questions.
Question 6:
Solve for the unknown in the following modular arithmetic equations:
a) 3m−2≡1(mod3)
Step 1: Add 2 to both sides of the congruence.
3m≡1+2(mod3)
3m≡3(mod3)
Step 2: Simplify the right side. Since 3≡0(mod3), we have:
3m≡0(mod3)
Step 3: Since 3m is always a multiple of 3, 3m≡0(mod3) is true for any integer