Question

Among six persons A, B, C, D, E, F who is the tallest? Statement (I): C is taller than only two persons, B is taller than A, and E is taller than only F.
Statement (II): A is shorter than two persons only, E is taller than F but shorter than C, C is shorter than A, and B is shorter than D.

• A. Statement (I) alone is sufficient.
• B. Statement (II) alone is sufficient.
• C. Both statements (I) and (II) are sufficient.
• D. Neither statement is sufficient.

Hint:

Always use rank slots (1st to 6th) to map the relationships given in ranking logic puzzles.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The task is to simplify the given Boolean expression \(A + \bar{A}B\) by applying standard Boolean algebra laws.


Step 2: Key Formula or Approach:
We will apply the Distributive Law:
\[ X + YZ = (X + Y)(X + Z) \] Along with the Complement Law (\(X + \bar{X} = 1\)) and the Identity Law (\(1 \cdot Y = Y\)).


Step 3: Detailed Explanation:
Start with the original expression:
\[ A + \bar{A}B \] Using the Distributive Law, we can expand this as:
\[ A + \bar{A}B = (A + \bar{A})(A + B) \] According to the Complement Law, a variable ORed with its inverse equals 1 (\(A + \bar{A} = 1\)). Substituting this yields:
\[ (1)(A + B) \] By the Identity Law, multiplying by 1 does not change the expression, so we are left with:
\[ A + B \]

Step 4: Final Answer:
The correct choice is (B).