We need to find the group:
[tex]P\cup(Q\cap R_{})[/tex]There are two group operations we need to perform. One is the intersection between two groups, which means that the resultant group will only have the members that are present on both groups and the union of two groups which means that the resultant group will have all the members of each group. We need to perform the one marked by parenthesis first. So we have:
[tex]\begin{gathered} Q\text{ = }\left\lbrace 2,6,13\right\rbrace \\ R\text{ = }\left\lbrace 3,6,9,13\right\rbrace \\ Q\cap R\text{ = }\left\lbrace 6,13\right\rbrace \end{gathered}[/tex]We now need to apply the "union" from that group with the group P.
[tex]P\cup(Q\cap R)\text{ = }\left\lbrace 6,9,10,13,14,15\right\rbrace [/tex]