When we throw a die, it can result in any one of the six number $1,2,3,4,5,6$,
and $S=\{1,2,3,4,5,6$,
(i) $A$ : a number less than $7=\{1,2,3,4,5,6\}$
(ii) $B:$ a number greater than $7=\{\}=\phi$
(iii) $C:$ a multiple of $3=\{3,6\}$
(iv) $D:$ a number less than $4=\{1,2,3\}$
(v) $E$ : an even number greater than $4=\{6\}$
(vi) $F$ : a number not less than $3=\{3,4,5,6\}$
$\therefore A \cup B=\{1,2,3,4,5,6\} \cup \phi=\{1,2,3,4,5,6\}$
$A \cap B=\{1,2,3,4,5,6\} \cap \phi=\phi$
$E \cup F=\{6\} \cup\{3,4,5,6\}=\{3,4,5,6\}$
$D \cap E=\{1,2,3\} \cap\{6\}=\{\phi\}$
$A-C=\{1,2,3,4,5,6\}-\{3,6\}=\{1,2,4,5\}$
$D-E=\{1,2,3\}-\{6\}=\{1,2,3\}$
$F=\{3,4,5,6\}$
$F^{\prime}=\{1,2,3,4,5,6\}-\{3,4,5,6\}=\{1,2\}$
$E \cap F^{\prime}=\{6\}-\{1,2\}=\phi$