Answer:
[tex]B = \{3,4,5,6\}[/tex]
Step-by-step explanation:
Given
[tex]A = \{1,2,3,4,5\}[/tex]
[tex]A\ n\ B = \{3,4,5\}[/tex]
[tex]A\ u\ B = \{1,2,3,4,5,6\}[/tex]
Required
Find set B
[tex]A\ n\ B = \{3,4,5\}[/tex] means that the common elements in A and B are 3, 4 and 5.
This implies that:
A subset of B are:
[tex]x = \{3,4,5\}[/tex]
And it also means that [tex]\{1,2\}[/tex] are not elements of B.
The remaining elements (y) of B are then calculated as follows:
[tex]y = (A\ u\ B) - (\{1,2\}\ u\ x)[/tex]
This gives:
[tex]y = \{1,2,3,4,5,6\} - (\{1,2\} u \{3,4,5\})[/tex]
[tex]y = \{1,2,3,4,5,6\} - \{1,2,3,4,5\}[/tex]
Remove common elements
[tex]y = \{6\}[/tex]
Hence, the set B is:
[tex]B = \{\{x\},\{y\}\}[/tex]
[tex]B = \{3,4,5,6\}[/tex]
