Q:

Applying set operations on subsets of $\{0, 1, 2, \ldots, 8, 9\}$

Set Operation- 
Let A={2,4,5,6,8} B={1,4,5,9} and c={x| E Z{positive Integer} and 2 <= x <5 } of S={0,1,2,3,4,5,6,7,8,9}
compute each of the following sets:
(c ∩ B)∪ ¬A
my answer:
C={0,1,2}
C ∩ B= {1}
¬A={0,1,3,7,9}
(c ∩ B)∪ ¬A = {0,1,3,7,9}
¬{B - A} ∩ (A - B)
¬{B - A}={0,2,3,4,5,6,7,8}
(A - B)={2,6,8}
¬{B - A} ∩ (A - B)= {0,2,3,4,5,6,7,8}
is this correct? also does any one know an online calculator I can verify these sets operations with . thank you 

A:

On your first, you got off to a bad start, since $$C =\{x\mid x \in \mathbb Z, 2\leq x \lt 5\} = \{2, 3, 4\}$$
In the second, you did fine until the end: you erred on your last step. You are being asked what the intersection of the two sets, not their union: $$\lnot(B-A) \cap (A-B) = \{2, 6, 8\}$$

