(b) Partition A = {1,2,3,4,5,6,7} rvith the minsets generated by Br = {.2,4,6} and B2 = {1,4,5} and also find out hou' manl different subsets of A can )rou generate lrom B. and B2? Expert's answer

Question:

Partition A = {1,2,3,4,5,6,7} with the minsets generated by $B_1 = \{2,4,6\}$ and $B_2 =\{1,4,5\}$.

Find out how many different subsets of A can you generate from $B_1$ and $B_2$ ?

Solution:

A = {1,2,3,4,5,6,7}, $B_1 = \{2,4,6\}$, $B_2 =\{1,4,5\}$

$B_1\cap B_2=\{4\}\\ B_1\cap {B_2}^c=\{2,6\}\\ {B_1}^c\cap {B_2}=\{1,5\}\\ {B_1}^c\cap {B_2}^c=\{3,7\}\\$