$2.$ Tic$-$Tac$-$Toe Strategy

Develop a set of rules for playing tic$-$tac$-$toe. Use the grid below $($numbered $1-9)$ to reference moves. Player $1$ moves first and uses X$.$ Player $2$ moves second and uses $0.$ Assume that both players are intentional with their moves and do not move randomly.

A$.$ Assume that Player $1$ places an X in the upper$-$left corner $($square $1).$ Explain how Player $1$ can force a win in each of the following cases.

Provide visuals with your discussion.

a$.$ Case $1$: Player $2$ plays in center top row $($square $2)$

b$.$ Case $2$: Player $2$ plays in the lower right corner $($square $9)$

c$.$ Case $3$: Player $2$ plays in the center bottom row $($square $8)$

d$.$ Case $4$: Player $2$ plays in the lower left corner $($square $7).$

B$.$ Assume that Player $1$ places an X in the upper$-$left corner $($square $1).$ What square should Player $2$ take in order to force a tie? Provide visuals with your discussion.

C$.$ Assume that Player $1$ places X in the center $($square $5).$ Is there a way to force Player $2$ to lose? Consider a few cases. Provide visuals with your discussion.