# $A=\{1,2,3,4,5\},B=\phi,C=\{3,6\},D=\{1,2,3\},E=\{6\},F=\{3,4,5,6\}$.Find $A \cup B,A\cap B,B \cup C,E \cap F,D\cap E,A-C,D-E,E \cap F',F'$

$A\cup B$=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"
$\Rightarrow \{1,2,3\}-\{6\}=\{1,2,3\}$
$E \cap F'=E \cap (\cup -F)$
$\Rightarrow E \cap [\{1,2,3,4,5,6\}-\{3,4,5,6\}]$
$[\cup =\{1,2,3,4,5,6\}]$
$\Rightarrow \{6\} \cap \{1,2\}$
$\Rightarrow \phi$
$F'=(\cap -F)=\{1,2,3,4,5,6\}-\{3,4,5,6\}$
$\Rightarrow \{1,2\}$