Step 1: Work with the potential difference across each diode:
Define the voltage across the diode as $V_D = V_p - V_n$. A positive $V_D$ means forward bias, and a negative $V_D$ means reverse bias.
Step 2: Compute $V_D$ for all four cases:
(A) $V_D = 5 - 10 = -5$ V.
(B) $V_D = -1.0 - (-1.5) = +0.5$ V.
(C) $V_D = 0 - 1 = -1$ V.
(D) $V_D = -2 - 0 = -2$ V.
Step 3: Read the signs:
Only (B) has a positive $V_D$. The current in a diode flows from p to n, and it flows only when the p-side is more positive.
Step 4: Note on the negative values:
A negative terminal voltage does not by itself mean reverse bias. What matters is the difference. In (B) both terminals are negative, yet the p-side is less negative, so the diode conducts.
Final Answer:
The forward biased diode is the one in option (B).
\[ \boxed{\text{Option (B)}} \]