Question

What will be the postfix equivalent of the expression (A + B)* (C - D)?

• A. A B + C D - *
• B. A B * C D + -
• C. A B - C D * +
• D. A B C * + D -

Hint:

Convert each bracket to postfix first: AB+ and CD-. Then put * after both.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
In postfix notation the operator comes after its two operands. Brackets are removed, and the order of operations is fixed by the position of the operators.

Step 2: Method.
Convert the part inside each bracket first. Then join the two results with the middle operator.

Step 3: Convert the brackets.
\(A + B\) becomes \(A\,B\,+\).
\(C - D\) becomes \(C\,D\,-\).

Step 4: Join with the multiplication.
The main operator is \(*\). Postfix puts it after both parts:
\[ A\,B\,+\;C\,D\,-\;* \]

Step 5: Check option 1 (A B + C D - *).
This is exactly what we got. So option 1 is correct.

Step 6: Check option 2 (A B * C D + -).
The operators are in the wrong places. It means (A * B) followed by C, D, +, -, which is not our expression. So it is wrong.

Step 7: Check option 3 (A B - C D * +).
This means (A - B) + (C * D), which has different operators. So it is wrong.

Step 8: Check option 4 (A B C * + D -).
This means A + (B * C) - D. The brackets of the original expression are ignored, so it is wrong.

Step 9: Final Answer:
The postfix form is A B + C D - *, which is option 1. \[ \boxed{A\,B\,+\,C\,D\,-\,*} \]