Processes $A$ and $B$

Considering an ideal gas, all you have to remember is that the slope of an adiabatic curve is steeper than that of an isothermal curve. An adiabatic process is one in which no heat is supplied to the system nor extracted from it. An isothermal process is one in which the system is at a constant temperature.

For an adiabatic (reversible) process: $PV^{n} = Constant$ , where $n = \frac{\text{Molar heat capacity at constant pressure}}{\text{Molar heat capacity at constant volume}}$

For an isothermal process: $PV = Constant$

So you can verify the first statement, mathematically.

Graphically, you can draw a line parallel to the $x$ -axis and observe that for the same pressure, $V_{B} < V_{A}$ .

In an adiabatic expansion, the temperature decreases by some amount while in an isothermal one it stays the same. If we assume this is an ideal gas. P1 V=nRT for adiabatic and P2 V=nR(T-s) Then P2 is smaller than P1.