Step 1: Keynes lists transaction, precautionary, and speculative demand, so (A) is correct.
Step 2: Transaction and precautionary demand depend on income, but speculative demand depends on the interest rate.
Step 3: Speculative demand rises when interest rates fall, an inverse link, not a positive function of income.
Step 4: So (R) is false.
\[ \boxed{\text{Option (3): (A) is true, (R) is false}} \]