Given the below set of documents $($D$1-$D$6),$

$$ Doc $1$ breakthrough material for research

$$ Doc $2$ new research material for research students

$$ Doc $3$ A new approach for research and new breakthrough material

$$ Doc $4$ Many new challenges for research students

$$ Doc $5$ Breakthrough the research barrier

$$ Doc $6$ Challenging the breakthroughs of past researchers

Stopword list $\{$a$,$ for, many, of$,$ at$,$ as$,$ each, past, the, on$,$ is$,$ was, will, who$\}$

$1.$ Using Boolean Method get the following Query. Use the mathematical calculations of boolean method and do it in step by along with the tabular colums also.

a$.$ Research AND students

b$.$ Breakthrough AND research OR method

c$.$ New OR approach AND break OR through