Boolean logic: Difference between revisions

Revision as of 21:10, 20 January 2011

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*In certain cases, '''AND''' and '''OR''' can be used interchangeably in English: ''I always carry an umbrella for when it rains '''and''' snows'' has the same meaning as ''I always carry an umbrella for when it rains '''or''' snows''. An alternate phrasing would be ''I always carry an umbrella for when precipitation is forecast.''

*Sometimes theThe English words "and" and "or" have a meaning that isusually apparentlyapplies oppositemore to ''sets of itsthings'' meaningthan inspecific booleancharacteristics logicof items: "Give me all the red '''and''' blue berries" usually means, "Give me... all the red berries that are '''eitherand''' redall '''or'''the blue berries". AnOnly alternativein phrasingthe forcontext thisof requesta wouldconversation be,about "Givethe mecharacteristics allof berries thatwould arethe redsame phrase mean "... and all the berries that arehave both red '''and''' blue. markings".

*Depending on the context, the word "or" may correspond with either logical '''OR''' (which corresponds to the English equivalent "and/or") or logical '''XOR''' (which corresponds to the English equivalent "either/or"):

** ''The waitress asked, "Would you like cream '''or''' sugar with your coffee?"'' This is an example of a "Logical '''OR'''", whereby the choices are cream, sugar, or cream and sugar (in addition to none of the above). This is an example of '''set''' taking precedence over '''item'''. The set of ''cream'' and ''sugar'' remains a set whether ''and'' or ''or'' are intended.

** ''The waitress asked, "Would you like soup '''or''' salad with your meal?"'' This is an example of a "Logical '''XOR'''", whereby the choices are soup or salad (or neither), but soup '''and''' salad are not an option.) This is '''item''' taking precedence over '''set'''.

** This can be a significant challenge when providing precise specifications for a computer program or electronic circuit in English. The description of such functionality may be ambiguous. Take for example the statement, "The program should verify that the applicant has checked the male '''or''' female box." This is usually interpreted as an '''XOR''' and so a verification is performed to ensure that one, and only one, box is selected. In other cases the intended interpretation of English may be less obvious; the author of the specification should be consulted to determine the original intent.