Boolean expression

<h2 id="boolean-operators">Boolean operators</h2>
<p>Most <a href="/facts/Programming_language/cWTYbgWa">programming languages</a> have the Boolean operators <a href="/facts/Logical_disjunction/jbI2EGlM">OR</a>, <a href="/facts/Logical_conjunction/62uyyn1d">AND</a> and <a href="/facts/Negation/q5AQBvBj">NOT</a>; in <a href="/facts/C_(programming_language)/Ky2No763">C</a> and some <a href="/facts/List_of_C-family_programming_languages/Pn4W8RB3">languages inspired by it</a>, these are represented by "||" (double pipe character), "&&" (double <a href="/facts/Ampersand/emmXUXuB">ampersand</a>) and "!" (<a href="/facts/Exclamation_mark/joGCCBau">exclamation point</a>) respectively, while the corresponding <a href="/facts/Bitwise_operation/0gkqnUda">bitwise operations</a> are represented by "|", "&" and "~" (tilde).<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a>  In the mathematical literature the symbols used are often "+" (<a href="/facts/Plus_sign/6RJD4Xt9">plus</a>), "·" (<a href="/facts/Full_stop/w0Ylafwn">dot</a>) and <a href="/facts/Overbar/PH46XuIu">overbar</a>, or "∨" (<a href="/facts/Descending_wedge/XX5LnH2H">vel</a>), "∧" (<a href="/facts/Wedge_(symbol)/fkN76mkJ">et</a>) and "¬" (<a href="/facts/Negation/q5AQBvBj">not</a>) or "′" (prime).
</p><p>Some languages, e.g., <a href="/facts/Perl/fx31kjlT">Perl</a> and <a href="/facts/Ruby_(programming_language)/BeYSaPSR">Ruby</a>, have two sets of Boolean operators, with identical functions but different precedence. Typically these languages use and, or and not for the lower precedence operators.
</p><p>Some programming languages derived from <a href="/facts/PL%2fI/469mVYgd">PL/I</a> have a bit string type and use BIT(1) rather than a separate Boolean type. In those languages the same operators serve for Boolean operations and bitwise operations. The languages represent OR, AND, NOT and EXCLUSIVE OR by "|", "&", "¬" (infix) and "¬" (prefix).
</p>
<h3>Short-circuit operators</h3>
<p class="note">Main article: <a href="/facts/Short-circuit_evaluation/GYhompFd">Short-circuit evaluation</a></p>
<p>Some programming languages, e.g., <a href="/facts/Ada_(programming_language)/Y2yHel4l">Ada</a>, have <a href="/facts/Short-circuit_evaluation/GYhompFd">short-circuit</a> Boolean operators. These operators use a <a href="/facts/Lazy_evaluation/mD3DxDkc">lazy evaluation</a>, that is, if the value of the expression can be determined from the left hand Boolean expression then they do not evaluate the right hand Boolean expression. As a result, there may be <a href="/facts/Side_effect_(computer_science)/AU3GlLzG">side effects</a> that only occur for one value of the left hand operand.
</p>
<h2 id="examples">Examples</h2>
<ul><li>The expression 5 > 3 is evaluated as <016 style="padding-left:0.4em; padding-right:0.4em; color:var( --color-subtle, #666666);">true.</li>
<li>The expression 3 > 5 is evaluated as <016 style="padding-left:0.4em; padding-right:0.4em; color:var( --color-subtle, #666666);">false.</li>
<li>5>=3 and 3<=5 are equivalent Boolean expressions, both of which are evaluated as <016 style="padding-left:0.4em; padding-right:0.4em; color:var( --color-subtle, #666666);">true.</li>
<li>Of course, most Boolean expressions will contain at least one variable (X > 3), and often more (X > Y).</li></ul>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Expression_(computer_science)/eRlhoBeN">Expression (computer science)</a></li>
<li><a href="/facts/Expression_(mathematics)/MPrMlYbE">Expression (mathematics)</a></li>
<li><a href="/facts/Boolean_function/uT7E8pqC">Boolean function</a></li></ul>

<h2 id="external-links">External links</h2>
<ul><li><a href="http://www.maths.tcd.ie/pub/HistMath/People/Boole/CalcLogic/CalcLogic.html">The Calculus of Logic</a>, by George Boole, Cambridge and Dublin Mathematical Journal Vol. III (1848), pp. 183–98.</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Gries, David; Schneider, Fred B. (1993), "Chapter 2. Boolean Expressions", A Logical Approach to Discrete Math, Monographs in Computer Science, Springer, p. 25ff, ISBN 9780387941158. <a href="9780387941158" target="_blank">9780387941158</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>van Melkebeek, Dieter (2000), Randomness and Completeness in Computational Complexity, Lecture Notes in Computer Science, vol. 1950, Springer, p. 22, ISBN 9783540414926. <a href="9783540414926" target="_blank">9783540414926</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>E.g. for Java see Brogden, William B.; Green, Marcus (2003), Java 2 Programmer, Que Publishing, p. 45, ISBN 9780789728616. <a href="9780789728616" target="_blank">9780789728616</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
</ol>

Boolean expression open-in-new

Boolean expression