Welcome to our community

Be a part of something great, join today!

Set Identity Proof

gicm

New member
Jan 28, 2019
1
Show that(A-B)-C=A-(BUC)
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,492
This can be shown using identities on sets. Two identities are: $A-B=A\bar{B}$ and $\overline{B\cup C}=\bar{B}\bar{C}$. Here $\bar{A}$ denotes the complement of $A$, and I skip intersection, i.e., I write $AB$ for $A\cap B$. There are numerous other identities on sets, such as commutativity and associativity of intersection and union, laws involving the empty set and so on. Can you use the ones I provided to prove your equality?