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or
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When two comparisons are connected using a ||, the entire expression is true provided that one or both of the comparisons are true; otherwise, the entire expression is false You can negate any Boolean expression using the ! operator If you want to negate a Boolean expression, place the expression in parentheses and place the ! operator in front of it For example, !(x < y) means x is not less than y The ! operator can usually be avoided For example, !(x < y) is equivalent to x >= y In some cases you can safely omit the parentheses, but the parentheses never do any harm The exact details on omitting parentheses are given in the subsection entitled Precedence Rules
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STRINGS
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OF INEQUALITIES
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Do not use a string of inequalities such as x < z < y If you do, your program will probably compile and run, but it will undoubtedly give incorrect output Instead, you must use two inequalities connected with an &&, as follows:
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(x < z) && (z < y)
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Flow of Control
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Display 21 Comparison Operators
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MATH SYMBOL = < > ENGLISH Equal to Not equal to Less than Less than or equal to Greater than Greater than or equal to C++ NOTATION
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== != < <=
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C++ SAMPLE
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MATH EQUIVALENT x + 7 = 2y
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> >=
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THE OR OPERATOR, ||
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You can form a more elaborate Boolean expression by combining two simpler Boolean expressions using the or operator, ||
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SYNTAX
FOR A
BOOLEAN EXPRESSION USING
(Boolean_Exp_1) || (Boolean_Exp_2)
EXAMPLE
WITHIN AN if-else STATEMENT
if ( (x == 1) || (x == y) ) cout << "x is 1 or x equals y\n"; else cout << "x is neither 1 nor equal to y\n";
If the value of x is equal to 1 or the value of x is equal to the value of y (or both), then the first cout statement will be executed; otherwise, the second cout statement will be executed (if-else statements are covered a bit later in this chapter, but the meaning of this simple example should be intuitively clear)
s EVALUATING BOOLEAN EXPRESSIONS
As you will see in the next two sections of this chapter, Boolean expressions are used to control branching and looping statements However, a Boolean expression has an independent identity apart from any branching or looping statement you might use it in A
Boolean Expressions
variable of type bool can store either of the values true or false Thus, you can set a variable of type bool equal to a boolean expression For example:
bool result = (x < z) && (z < y);
A Boolean expression can be evaluated in the same way that an arithmetic expression is evaluated The only difference is that an arithmetic expression uses operations such as +, *, and / and produces a number as the nal result, whereas a Boolean expression uses relational operations such as == and < and Boolean operations such as &&, ||, and ! and produces one of the two values true or false as the nal result Note that =, !=, <, <=, and so forth, operate on pairs of any built-in type to produce a Boolean value true or false First let s review evaluating an arithmetic expression The same technique will work to evaluate Boolean expressions Consider the following arithmetic expression:
(x + 1) * (x + 3)
Assume that the variable x has the value 2 To evaluate this arithmetic expression, you evaluate the two sums to obtain the numbers 3 and 5, and then you combine these two numbers 3 and 5 using the * operator to obtain 15 as the nal value Notice that in performing this evaluation, you do not multiply the expressions (x + 1) and (x + 3) Instead, you multiply the values of these expressions You use 3; you do not use (x + 1) You use 5; you do not use (x + 3) The computer evaluates Boolean expressions the same way Subexpressions are evaluated to obtain values, each of which is either true or false These individual values of true or false are then combined according to the rules in the tables shown in Display 22 For example, consider the Boolean expression
!( ( y < 3) || (y > 7) )