# Math Help - Symmetric Difference

1. ## Symmetric Difference

The symmetric difference of A and B is
(a) $(A-B) \cap (B-A)$
(b) $(A-B)\cup (B-A)$
(c) $(A \cup B) - (A \cap B)$
(d) $\{(A \cup B)-A\} \cup \{(A \cup B)-B\}$

Its answer given in the book is (b). But I found that (c) and (d) are also true. Am I right? If not please tell why. Thanks a lot for giving me your time.

2. ## Symmetric Difference

Hello ninni
Originally Posted by ninni
The symmetric difference of A and B is
(a) $(A-B) \cap (B-A)$
(b) $(A-B)\cup (B-A)$
(c) $(A \cup B) - (A \cap B)$
(d) $\{(A \cup B)-A\} \cup \{(A \cup B)-B\}$

Its answer given in the book is (b). But I found that (c) and (d) are also true. Am I right? If not please tell why. Thanks a lot for giving me your time.
You are right. (a) is the only expression not equal to the symmetric difference of the sets A and B.

3. Originally Posted by ninni
The symmetric difference of A and B is
(a) $(A-B) \cap (B-A)$
(b) $(A-B)\cup (B-A)$
(c) $(A \cup B) - (A \cap B)$
(d) $\{(A \cup B)-A\} \cup \{(A \cup B)-B\}$

Its answer given in the book is (b). But I found that (c) and (d) are also true. Am I right? If not please tell why. Thanks a lot for giving me your time.
Yes you are right about (c).[I dindn'ttry to prove the others].
One of the proofs of (c):