One mole of ideal gas is in a piston pipe with the initial conditions of temperature T_0, pressure, P_0, and volume, V_0.
(1) At constant temperature conditions, if the volume decreases to become \frac{1}{2}V_0, the pressure eventually increases to 2P_0
(2) At constant pressure conditions, if the temperature increases to 2T_0 , then the volume eventually decreases to \frac{1}{2}V_0
(3) At fixed volume conditions, if the pressure increases to 3P_0, the temperature eventually increases to 3T_0
Which are the correct statements regarding the above phenomenon?
a. (1) and (2)
b. (1) and (3)
c. (2) and (3)
d. (1), (2), and (3)
e. Neither is true