1. The problem asks to identify the law in Boolean algebra where a variable ANDed with 0 results in 0, and a variable ORed with 1 results in 1. 2. This is a fundamental property in Boolean algebra known as the Annulment Law. 3. The Annulment Law states: - $x \cdot 0 = 0$ - $x + 1 = 1$ 4. Therefore, the correct answer for question 4 is the Annulment law. 5. The second problem asks to minimize the Boolean expression $F = xyz' + xy'z + x'yz' + x'y'z + x'y'z' + xy'z$ using a 3-variable Karnaugh map. 6. Let's analyze the terms: - $xyz'$ means $x=1, y=1, z=0$ - $xy'z$ means $x=1, y=0, z=1$ - $x'yz'$ means $x=0, y=1, z=0$ - $x'y'z$ means $x=0, y=0, z=1$ - $x'y'z'$ means $x=0, y=0, z=0$ - $xy'z$ (repeated) means $x=1, y=0, z=1$ 7. Plotting these on a Karnaugh map and grouping the ones, the minimized expression is: $$F = x'y' + y'z + yz'$$ 8. This matches the first option in question 5. 9. Therefore, the correct answer for question 5 is $x'y' + y'z + yz'$. Final answers: - Question 4: Annulment law - Question 5: $x'y' + y'z + yz'$