Question

Find the sum

(1) 4 ⊕₅ 3

(2) 5 ⊕₇ 4

(3) (3 ⊕₇ 6) ⊕₇ 4

(4) (10 ⊕₁₂ 2) ⊕₁₂ 3

Answer 1

means r is the remainder when (a + b) is divided by m.

(1)

Here, 4 + 3 = 7

Upon dividing 7 by 5, we get the remainder as 2.

Hence,

(2)

Here, 5 + 4 = 9

Upon dividing 9 by 7, we get the remainder as 2.

Hence,

(3)

To simplify the given expression, simplify the bracket first.

Consider.

Here, 3 + 6 = 9

Upon dividing 9 by 7, we get the remainder as 2.

∴

∴

Now, 2 + 4 = 6

Since 6 < 7,

Hence,

(4)

To simplify the given expression, simplify the bracket first.

Consider.

Here, 10 + 2 = 12

Upon dividing 12 by 12, we get the remainder as 0.

∴

∴

Since 0 + 3 = 3 < 12,

Hence,