Consider the following infix expression Q: ((A+B) *D) ↑ (E-F). The equivalent postfix expression of Q is
Solution
The correct answer is Option 4) A B + D * E F − ↑
Key Points
- We must convert the infix expression
Q = ((A + B) * D) ↑ (E − F) to postfix (Reverse Polish) form.
- Operator facts used:
- Parentheses force evaluation of the enclosed subexpression first.
- Precedence:
↑ (exponent) > * > +/−.
↑ is right-associative; *, +, − are left-associative.
- Postfix rule: write the postfix of each operand/subexpression, then append the operator.
Step-by-step conversion (by subexpressions)
- Left inner parentheses:
(A + B) → postfix is AB+.
- Multiply by
D: ((A + B) * D) → append D then * ⇒ AB+D*.
- Right inner parentheses:
(E − F) → postfix is EF-.
- Exponent between the two big operands:
Left operand’s postfix = AB+D*, right operand’s postfix = EF-.
Append the operator ↑ ⇒ AB+D* EF- ↑.
Final postfix
A B + D * E F − ↑
Quick verification via stack method (tokens scanned left→right)
Output: A B + D * | Stack after handling left side: ( ^ )
Output: A B + D * E F - | Pop ^ at end → A B + D * E F - ↑
Thus, the equivalent postfix expression of ((A+B)*D) ↑ (E−F) is A B + D * E F − ↑ (Option 4).