Question

Which one of the following is prefix representation of the infix expression \(P*(Q+R)/S\)?

• A. \(/ * P + Q R S\)
• B. \(P+Q/R*S\)
• C. \(*+*PQ/RS\)
• D. \(/+QR*PS\)

Hint:

Prefix notation places operators before operands. Example: \[ (A+B) \rightarrow +AB \] \[ (A+B)*C \rightarrow *+ABC \]

Answer 1

The Correct Option is A

Concept: Prefix notation places the operator before its operands. To convert infix to prefix:
• Evaluate brackets first.
• Move operators before operands.
• Preserve precedence.

Step 1: Given expression.
\[ P*(Q+R)/S \] The bracketed part is \[ (Q+R) \] whose prefix form is \[ +QR \]

Step 2: Multiply with \(P\).
\[ P*(Q+R) \] becomes \[ *P(+QR) \] or \[ *P+QR \]

Step 3: Divide by \(S\).
\[ \frac{P*(Q+R)}{S} \] becomes \[ /(*P+QR)S \] or \[ \boxed{/*P+QRS} \]

Step 4: Select the answer.
Hence option (A) is correct.