Let T = {1, . . . , 12} × {0, 1, . . . , 59} denote the set of numbers that can be displayed on a digital clock in twelve-hour mode. Define a function add : T × Z≥0 → T so that add(t, x) denotes the...

Let T = {1, . . . , 12} × {0, 1, . . . , 59} denote the set of numbers that can be displayed on a digital clock in twelve-hour mode. Define a function add : T × Z^≥0
→ T so that add(t, x) denotes the time that’s x minutes later than t. Do so using only standard symbols from arithmetic.