Please provide a truth table for the rules described above and a Schematic diagram and non

simplified boolean expression based on the truth table. What gates should be use?

$[$Description of $"$On $-$ Off" logic game$]$

Three persons named X$,$ Y$,$ and Z participate the game called $"$On $-$ Off". Each person has

his$/$her own electronic switch, and everyone will turn ON or turn OFF the switch all at

once when a commander gives a start command. They will win the game if one of the

following three cases $(1)$ through $(3)$ is true. Otherwise, they will lose the game.

$(1)$ Person $x$ turns ON$,$ Person Y and Person Z turn OFF

$(2)$ Person $x$ and Person $Z$ turn ON$,$ Person Y turns OFF

$(3)$ Person $Y$ turns ON$,$ Person $x$ and Person $Z$ turn OFF