Return to Answer

Player-A says p is possible, exactly when player A can see someone who raises their hand for p. That means, when player-A says p is possible, then player-A can see someone.

Player A says q is necessary, exactly when everyone player-A can see raises their hand for q.

Thus if player-A can see someone, then if everyone player-A can see raises their hand for q, then player-A can see someone who raises their hand for q.

Mp -> (Lq -> Mq)

exercise 1.2: show that in any seating arrangement in which there's a player who cannot see himself Lp->p isn't valid.

 

My answer: Suppose A cannot see himself. Let p be on every player's sheet except A's. Suppose that A raises his hand for Lp->p then he must raise his hand for p, since he raised his hand for Lp, but he cannot see everyone's sheet (only his own), so he should keep his hand down for p, and we get that Lp->p isn't valid.

 

Is my reasoning ok or not?

It is not. The criteria is that the player cannot see his self.

Player-A says p is possible, exactly when player A can see someone who raises their hand for p. That means, when player-A says p is possible, then player-A can see someone.

Player A says q is necessary, exactly when everyone player-A can see raises their hand for q.

Thus if player-A can see someone, then if everyone player-A can see raises their hand for q, then player-A can see someone who raises their hand for q.

Mp -> (Lq -> Mq)

exercise 1.2: show that in any seating arrangement in which there's a player who cannot see himself Lp->p isn't valid.

My answer: Suppose A cannot see himself. Let p be on every player's sheet except A's. Suppose that A raises his hand for Lp->p then he must raise his hand for p, since he raised his hand for Lp, but he cannot see everyone's sheet (only his own), so he should keep his hand down for p, and we get that Lp->p isn't valid.

Is my reasoning ok or not?

It is not. The criteria is that the player cannot see his self.

Player-A says p is possible, exactly when player A can see someone who raises their hand for p. That means, when player-A says p is possible, then player-A can see someone.

Player A says q is necessary, exactly when everyone player-A can see raises their hand for q.

Thus if player-A can see someone, then if everyone player-A can see raises their hand for q, then player-A can see someone who raises their hand for q.

Mp -> (Lq -> Mq)

Player-A says p is possible, exactly when player A can see someone who raises their hand for p. That means, when player-A says p is possible, then player-A can see someone.

Player A says q is necessary, exactly when everyone player-A can see raises their hand for q.

Thus if player-A can see someone, then if everyone player-A can see raises their hand for q, then player-A can see someone who raises their hand for q.

Mp -> (Lq -> Mq)

exercise 1.2: show that in any seating arrangement in which there's a player who cannot see himself Lp->p isn't valid.

My answer: Suppose A cannot see himself. Let p be on every player's sheet except A's. Suppose that A raises his hand for Lp->p then he must raise his hand for p, since he raised his hand for Lp, but he cannot see everyone's sheet (only his own), so he should keep his hand down for p, and we get that Lp->p isn't valid.

Is my reasoning ok or not?

It is not. The criteria is that the player cannot see his self.

Opps. I mixed up the p and ps.

Player-A says p is possible, exactly when player A can see someone who raises their hand for p. That means, when player-A says p is possible, then player-A can see someone.

Player A says q is necessary, exactly when everyone player-A can see raises their hand for q.

Thus if player-A can see someone, then if everyone player-A can see raises their hand for q, then player-A can see someone who raises their hand for q.

Mp -> (Lq -> Mq)