1. Determine the sets $A$ and $B$ for which the following conditions are simultaneously satisfied:
i) $A \cup B=\{1,2,3,4,5,6\}$;

ii) $A \backslash B=\{1,3,5\}$;

iii) $B \backslash A=\{2,6\}$.

Supliment, G.M., December 2013
## Solution:

$\operatorname{From} A \backslash B=\{1,3,5\} \Rightarrow 1,3,5 \in A$ and $1,3,5 \notin B$ $2 p$

From $B \backslash A=\{2,6\} \Rightarrow 2,6 \in B$ and $2,6 \notin A$ $2 p$

$A=\{1,3,5,4\}, B=\{2,6,4\}$ $3 p$