Think of progesterone as a respiratory stimulant. It sensitises the brainstem respiratory centre to carbon dioxide, so for any given PCO2 the woman breathes more. The clinical correlate is the well-known dyspnoea/hyperventilation of normal pregnancy.
Because the extra ventilation comes chiefly from bigger breaths, tidal volume climbs by about a third while respiratory rate barely changes. That eliminates the option claiming a fall in tidal volume.
Greater alveolar ventilation washes out CO2, so arterial PCO2 drops to the high-20s to low-30s mmHg, giving a chronic respiratory alkalosis that the kidney compensates by excreting bicarbonate. Therefore the options claiming a rise in PCO2 are wrong. Oxygenation stays normal or improves marginally, so a fall in PO2 is also incorrect.
$\uparrow \text{progesterone} \Rightarrow \uparrow \text{respiratory drive} \Rightarrow \uparrow V_T \Rightarrow \downarrow PaCO_2$
\[\boxed{\text{Increased respiratory drive (hyperventilation)}}\]