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The elements of [tex]S = P\,\cap\,(Q\,\cup\,R)[/tex] are [tex]\{2,3,4\}[/tex].

How to determine the elements of a resulting set operation

Let [tex]P = \{1,2,3,4\}[/tex], [tex]Q = \{2,4,6,8\}[/tex], [tex]R= \{3, 4, 5, 6\}[/tex] and [tex]S = P\,\cap\,(Q\,\cup\,R)[/tex], the characteristics of the two fundamental operations between two sets are described below:

  1. A union between two sets consists in the creation of a set with all elements, common or not, of both. The operator symbol is [tex]\cup[/tex].
  2. An intersection between two sets consists in the creation of a set only with common elements.

Then, we have that the elements of [tex]S[/tex] are listed below:

[tex]S = \{1,2,3,4\}\,\cap\,(\{2,4,6,8\}\,\cup\,\{3,4,5,6\})[/tex]

[tex]S = \{1,2,3,4\}\,\cap\,\{2,3,4,5,6,8\}[/tex]

[tex]S = \{2,3,4\}[/tex]

The elements of [tex]S = P\,\cap\,(Q\,\cup\,R)[/tex] are [tex]\{2,3,4\}[/tex]. [tex]\blacksquare[/tex]

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