Chapter 12.1, Problem 3ES

### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

Chapter
Section

### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# If the expression a b + c d + ⋅ in postfix notation is converted to infix notation, what is the result? b. Let   ∑ = { 1 ,   2 ,   * ,   / } and let L be the set of all strings over ∑ obtained by writing first a number (1 or 2), then a second number (1 or 2), which can be the same as the first one, and finally an operation (denoted * or /, where * indicates multiplication and /indicates division). Then L is a set of postfix, or reverse Polish, expressions. List all the elements of L between braces, and evaluate the resulting expressions.

To determine

(a)

If the expression ab+cd+ in postfix notation is converted to infix notation, what is the result?

Explanation

Given information:

Infix notation, prefix notation, postfix notation

Concept used:

An expression such as a+b in which a binary operator such as + sits between the two quantities

on which it acts, is said to be written in infix notation.

If the operator precedes the quantities on which it acts, then it is called prefix notation.

If the operator follows the quantities on which it acts, then it is called postfix notation.

Calculation:

Given statement is in the postfix notation as ab+cd+.

Observe that + follows ab.

So, the actual operation is a+b

+ follows cd.

So, the actual operation is c+d

Dots '·' follows c+d

To determine

(b)

List all the element of L between braces and evaluate the resulting expression.

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