In an automatic chocolate vending machine, there are 2 push buttons pl and p2. When a button is pressed, the price of the product is displayed in a 7-segment display. If no buttons are pressed, '0' is displayed, specifying 0 OMR/-
If p1 is pressed, '2' is displayed, specifying 2 OMR/-
If p2 is pressed, '5' is displayed, specifying 5 OMR/-
If p1 and p2 are pressed, 'E' is displayed, specifying ERROR.
If segments a to g are considered as functions of p1 and p2:
a) Prove g = p1 + p2; d = c + e