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Chapter 3: Problem 113

If a symbolic statement does not contain parentheses, how are the grouping symbols determined?

Short Answer

Expert verified
The grouping symbols for an unparenthesized symbolic statement are determined by operator precedence. First, operations with higher precedence are grouped, then those with the same precedence are evaluated from left to right.

Step by step solution

01

Understand the precedence of operators

The grouping of symbols in a symbolic statement with no explicit parenthesis is determined by the precedence of the operators. Higher precedence operators are evaluated first. If two operators have the same precedence, then the expression is evaluated from left to right. For example, multiplication and division operators usually have higher precedence than addition and subtraction.
02

Apply the precedence rules

Group the parts of the statement that include higher precedence operators. For instance, in the symbolic statement \( A + B \times C \), \( B \times C \) has precedence due to the multiplication operator hence, it is evaluated first before the addition operation. Which is equivalent to \( A + (B \times C) \) were parentheses used.
03

Grouping symbols for same precedence operators

In the case where you have operators of the same precedence, evaluate from left to right. For example, the symbolic statement \( A - B + C \) is read as \( (A - B) + C \). Remember, this might not be the case for all languages or contexts, therefore it's essential to understand the specific rules of the system you're working in.

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