Question

use laws of algebra of sets to show (A-B)∪(B-A) =(A∪B)-(B∩A)

Answer 1

(A-B) UNION (B-A) = (A-B )

Answer 2

@briszabo But that's just wrong, or implies that B-A is the empty set.

Answer 3

ohh alright i just tried i didnt know it i was right but i also got this (A - B) UNION (B - A) = (A UNION B) - (B INTERSECT A) but then i got stuck with the rest

Answer 4

need help T_T

Answer 5

Let \(x\in (A-B)\cup(B-A)\). Then \(x\in A\) and \(x\notin B\) or \(x\in B\) and \(x\notin A\). If \(x\in A\) and \(x\notin B\), then \(x\in A\cup B\) and \(x\notin A\cap B\). Similarly, it follows if \(x\in B\) and \(x\notin A\). Hence, \((A-B)\cup(B-A)\subseteq(A\cup B)-(A\cap B)\).

You can how try and prove the converse.

Answer 6

ty anyways but thats not what i want T_T