I have no idea how to solve this. Any help would be appreciated! The statement is

For any setsA, B,andCthat are subsets of a universal setU, A-(B∩C)=(A-B)∪(A-C).

Printable View

- Apr 25th 2012, 03:05 PMgoalkeeper00Math Proof A-(B∩C)=(A-B)∪(A-C).
I have no idea how to solve this. Any help would be appreciated! The statement is

For any sets*A, B,*and*C*that are subsets of a universal set*U*, A-(B∩C)=(A-B)∪(A-C). - Apr 25th 2012, 03:11 PMigniteRe: Math Proof A-(B∩C)=(A-B)∪(A-C).
Use following properties:

X-Y=X∩Y'

(X∩Y)'=X'∪Y'

A-(B∩C)=A∩(B∩C)'=A∩(B'∪C')=(A∩B')∪(A∩C')=(A-B)∪(A-C) - Apr 25th 2012, 03:17 PMPlatoRe: Math Proof A-(B∩C)=(A-B)∪(A-C).
- Apr 27th 2012, 07:46 AMHallsofIvyRe: Math Proof A-(B∩C)=(A-B)∪(A-C).
Or use the basic definitions: if x is in $\displaystyle A-(B\cap C)$ then x is in A but not in $\displaystyle B\cap C$. That, in turn, means it is either NOT in B or NOT in C.

case 1: x is in A but not in B. Then it is in $\displaystyle A\cap B$.

case 2: x is in A but not in C. Then it is in $\displaystyle A\cap C$.