Question

prove: B-(B-A)=AintersectingB

Answer 1

hmmmm I can demonstrate this using venn diagrams but I doubt that is sufficient

Answer 2

@dan815 How can we solve this with a mathematical approach?

Answer 3

Make a truth table

Answer 4

wanna hang out?

Answer 5

\[B-A=B\cap A^{c}\]

Answer 6

\[B-(B-A)=B-B\cap A^{c}=B\cap (B\cap A^{c})^c\]

Answer 7

ahhhh yeaaaaa I remember doing this stuff

Answer 8

\[B\cap (B\cap A^{c})^c=B\cap (B^c\cup A)=(B\cap B^c)\cup(B\cap A)\]

\[=\emptyset\cup (B\cap A)=B\cap A\]