Step 1: Check the Assertion.
Sensible heating adds heat to air purely to raise its dry bulb temperature, without adding or removing any moisture, so the humidity ratio, that is the actual moisture content of the air, stays exactly the same. This means the claim that sensible heating increases humidity is incorrect, Assertion (A) is false.
Step 2: Check the Reason.
On a psychrometric chart, humidity ratio is read on the vertical axis. Since sensible heating changes temperature but keeps humidity ratio fixed, the process traces a straight horizontal line moving to the right at constant height on the chart, so Reason (R) is correct.
Step 3: Combine the findings.
Assertion (A) is false while Reason (R) is true.
\[ \boxed{(A) is false but (R) is true.} \]