A binary operation Δ is defined on the set $S = \{0, 1, 2, 3, 4\}$ by $a \Delta b = (a + b) \mod 5$. Find the inverse of 3 under this operation, given that the identity element is 0.

The inverse of 3 is the element x such that 3 Δ x = 0 (the identity). We need (3 + x) mod 5 = 0, so 3 + x must be a multiple of 5. With x = 2: (3 + 2) mod 5 = 5 mod 5 = 0. ✓ Thus the inverse of 3 is 2. Option D (x = 4) gives (3 + 4) mod 5 = 2, not 0.