$A\cup B$=This means elements which are in both A and B

$\Rightarrow \{1,2,3,4,5,6\} \cup \phi=\{1,2,3,4,5,6\}$

$A\cap B$=This means elements which are common in both A and B

$\Rightarrow \{1,2,3,4,5,6\} \cap \phi=\phi$

$B\cup C$=This means elements which are in both B and C

$\Rightarrow \phi \cup \{3,6\}=\{3,6\}$

$E\cap F$=This means elements which are common in both E and F

$\Rightarrow \{6\} \cap \{3,4,5,6\}=\{6\}$

$D\cap E$=This means elements which are common in both D and E

$\Rightarrow \{1,2,3\} \cap \{6\}=\phi$

$A-C$=This means "the elements which are in A but not in C"

$\Rightarrow \{1,2,3,4,5,6\}-\{3,6\}=\{1,2,4,5\}$

$D-E$=This means "the elements which are in D but not in E"

$\Rightarrow \{1,2,3\}-\{6\}=\{1,2,3\}$

$E \cap F'=E \cap (\cup -F)$

$\Rightarrow E \cap [\{1,2,3,4,5,6\}-\{3,4,5,6\}]$

$[\cup =\{1,2,3,4,5,6\}]$

$\Rightarrow \{6\} \cap \{1,2\}$

$\Rightarrow \phi$

$F'=(\cap -F)=\{1,2,3,4,5,6\}-\{3,4,5,6\}$

$\Rightarrow \{1,2\}$