True or False? "A social choice function that always chooses some predetermined option x is strategy-proof." Select one: True False True or False? "A social choice function that always chooses some predetermined option x violates Weak Pareto*." Select one: True False True or False? "A social choice function that always chooses some predetermined option x violates monotonicity." Select one: True False True or False? "A dictatorship* violates monotonicity." Select one: True False True or False? "A dictatorship" satisfies Weak Pareto*" Select one: True False