Question

Which of the following postfix expressions corresponds to the given infix expression?

(13 + 14 - 3 + 2) / 2 ^ 3

A.) 13 14 + 3 - 2 + 2 3 / ^
B.) 13 14 + 3 2 - + 2 3 ^ /
C.) 13 14 + 3 - 2 + 2 3 ^ /
D.) 13 14 + 3 2 + - 2 3 ^ /

Answer 1

To convert the infix expression (13 + 14 - 3 + 2) / 2 ^ 3 to postfix expression, we follow the order of operations and the resulting postfix expression is 13 14 + 3 - 2 + 2 3 ^ /. The correct answer is option C.

Step-by-step explanation:

To determine which postfix expression corresponds to the given infix expression (13 + 14 - 3 + 2) / 2 ^ 3, we must first evaluate the infix expression following the order of operations (parentheses, exponents, multiplication and division, addition and subtraction) and then convert that expression into post-fix (Reverse Polish notation).

Following the order of operations in the given infix expression, we first perform the operations inside the parentheses, which is a sequence of addition and subtraction:

1. 13 + 14 = 27
2. 27 - 3 = 24
3. 24 + 2 = 26

Next, we divide the result by 2 and then raise it to the power of 3:

1. 26 / 2 = 13
2. 13 ^ 3

In postfix notation, this would be converted as follows:

1. Add 13 and 14: 13 14 +
2. Subtract 3: 3 -
3. Add 2: 2 +
4. Divide by 2: 2 /
5. Raise to the power of 3: 3 ^

Putting it all together, we get the complete postfix expression as:

13 14 + 3 - 2 + 2 3 ^ /. The correct option is C.