Thermodynamic Processes

In an adiabatic process there is no exchange of heat between the system and the surroundings, i.e. $\Delta Q=0$. Hence heat is neither absorbed nor released in an adiabatic process.

Work done on the gas equals the area under the P–V curve; the adiabatic curve is the steepest, so it encloses the largest area.
$W_{isochoric} = 0$ and $W_{adiabatic} > W_{isothermal} > W_{isobaric}$

Isothermal expansion: PV = constant, so as the volume goes from V to 3V the pressure falls along a rectangular hyperbola.
Then the volume is reduced from 3V back to V at constant pressure: a horizontal straight line directed towards smaller volume.
So the diagram shows a falling hyperbola from A (at V) to 3V, followed by a horizontal line back to V ending at B, which lies below A.

Adiabatic process: no heat is exchanged, so the system is insulated from the surroundings, and for an ideal gas $PV^\gamma$ = constant. Both statements are true.
Isothermal process: the temperature remains constant (true).
Isochoric process: it is the volume that remains constant; the pressure changes with temperature ($P \propto T$).
The process in which pressure remains constant is the isobaric process.
Hence the statement that is not true is 'In an isochoric process pressure remains constant'.