Given sets A, B and C, if A
B
and AC,
prove or disprove the following:(B
C)
- A = (B - A) 
(C
- A)Set Properties and Definitions
B
and AC,
prove or disprove the following: C)
- A = (B - A) (C
- A)Proof using Venn diagrams.
As can be seen below, it is very easy to construct a Venn diagram which shows that the above set equivalency is false.
Using the venn diagrams as a starting point, show that there can be an element in one side of the equation that is not in the other.
Let A = {x}, let B = {w, x, y}, and let C = {w, x, z}.
Then, for the left side of the equation:
B C
= {w, x}; and
(B C)
- A = {w }.
For the right side of the equation:
B - A = {w, y};
C - A = {w, z}; and
(B - A) (C
- A) = {w, y, z}.
Putting the 2 halves together,
{w } 
{w,
y, z}
And so the equation has been proved false.
