Our reader’s question is: “There are two sets of signs for ‘union’ and also ‘intersection’. One is the and also the upside down, and also the various other set is the and the . What is the partnership in between these icons, which we periodically think of as ‘U’s and also ‘V’s?”

So let’s mind our Us and also Vs, and their upside-down companions, in unions and also intersections and logical features.

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The Math Symbols from the Inquiry about Union and Intersection

The “V” icons in the reader’s question are and , which suppose “Logical Or” and “Logical And.” The is a capital Greek Lambda.

The small ^or “caret” is easily accessible on most key-boards as “shift-6”; it symbolizes the exponentiation function. It is essential not to confusage ^with .

The symbol for “Union of sets” is ‘‘, while the symbol for “interarea of sets” is ‘∩.’

Set Theory for Union and also Intersection


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Math signs can be confusing! Image by JRS


Our reader’s question additionally asked about ‘V’ and also upside-dvery own ‘V’, ‘Λ’ or Lambda. These are provided in mathematical logic.

Let statement A = “All humans are mammals.” Let B = “All mammals are human beings.” Let C = “Some birds have the right to fly under some problems.” Both ‘A’ and ‘C’ are true statements, yet ‘B’ is false.

Let ‘X’ and ‘Y’ recurrent any kind of maybe true or false statements.

In the math of logic, the statement “X and Y”, or “XΛY”, is true if and just if both ‘X’ and also ‘Y’ are true.

However before, “X or Y”, or “XY”, is false if and just if both ‘X’ and ‘Y’ are false. “XY” is true if either ‘X’ or ‘Y’ is true, which has the situation where both ‘X’ and ‘Y’ are true.

From the instance statements, “AB”, “AC” and also “BC” are all true. However, “AΛB” and also “BΛC” are both false. Only “AΛC” is true bereason each of statements ‘A’ and ‘C’ are true.

Programming Computers via “And” and “Or”

Depending on the programming language, “X and Y” could be stood for as “X&&Y” fairly than “XΛY.” Likewise, “X or Y” could be shown as “X||Y” rather than “XY.”

Exponentiation through the Caret Symbol

The caret symbol, ‘^’, could be mistaken for lambda, ‘Λ’. However, it usually represents the exponentiation operation. For example, 2^3 = 2*2*2 = 8.

When creating on paper, or once the text editor supports superscript, the exponent is shown as a supermanuscript. See the picture above.

Rundown of Mathematical Symbols for Intersection and also Union, And and Or

In set concept, interarea and union are presented by ‘∩’ and also ‘‘. In mathematical logic, the “and” and “or” operations are displayed by ‘Λ’ and also ‘V’.

The union of sets, “AB”, can be seen as taking all the aspects of ‘A’ and also likewise the aspects of ‘B’; however that would not be the “and” (‘Λ’) of mathematical logic.

The interarea of sets, “A∩B” has actually also less to perform with a logical “or” (‘‘) operation.

Other areas of math might use these icons in various other ways, however these interpretations deal many straight via the reader’s question.

References:

Wolfram Mathematica Documentation. Intersection; Union; And; Or. (2012). Accessed July 26, 2012.

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Wood, Alan. Symbol font – Unicode options for Greek and unique personalities in HTML. (1997-2010). Accessed July 26, 2012.