By definition points \\(x\\) and \\(y\\) are connected if there are points \\(z_{1}...z_{n}\\) where \\(x\\) is connected to \\(z_{1}\\), \\(z_{i}\\) is connected to \\(z_{i+1}\\), and \\(z_{i+1}\\) is connected to \\(y\\).

Applying this to the problem:

\\(11\\) and \\(12\\) are connected in first set

\\(12\\) and \\(22\\) are connected in second set \\(\implies\\) \\(11\\) and \\(22\\) are connected

\\(22\\) and \\(23\\) are connected in first set

\\(23\\) and \\(13\\) are connected in second set \\(\implies\\) \\(13\\) and \\(22\\) are connected

\\(21\\) is isolated in both sets

Hence the join operation will result in two partitions, which are {11,12,13,22,23} and {21}

Applying this to the problem:

\\(11\\) and \\(12\\) are connected in first set

\\(12\\) and \\(22\\) are connected in second set \\(\implies\\) \\(11\\) and \\(22\\) are connected

\\(22\\) and \\(23\\) are connected in first set

\\(23\\) and \\(13\\) are connected in second set \\(\implies\\) \\(13\\) and \\(22\\) are connected

\\(21\\) is isolated in both sets

Hence the join operation will result in two partitions, which are {11,12,13,22,23} and {21}