1. **State the problem:** We need to find the value of the logical expression $$F = (A \text{ AND } B) \text{ OR } (A \text{ XOR } B)$$ given $$A=1$$ and $$B=0$$. 2. **Recall the logical operations:** - AND: $$A \text{ AND } B = 1$$ if both $$A=1$$ and $$B=1$$, else 0. - OR: $$A \text{ OR } B = 1$$ if at least one of $$A$$ or $$B$$ is 1. - XOR (exclusive OR): $$A \text{ XOR } B = 1$$ if exactly one of $$A$$ or $$B$$ is 1, else 0. 3. **Calculate each part:** - $$A \text{ AND } B = 1 \times 0 = 0$$ - $$A \text{ XOR } B = 1$$ (since exactly one is 1) 4. **Combine with OR:** - $$F = 0 \text{ OR } 1 = 1$$ **Final answer:** $$F=1$$