Answer
a) A ⊕ B= (A - B) U (B - A)= (B-A) U (A-B)= B⊕A
b) (A⊕B) ⊕B = ((a U c) ⊕ (b U c)) ⊕ ( b U c)
=(a U b) ⊕ (b U c)
=(a U c)
=A
Work Step by Step
The symmetric difference of A and B, denoted by A ⊕ B,is
the set containing those elements in either A or B, but not in
both A and B. so as we know that A⊕B=(A−B)∪(B−A) and the commutative laws (A U B)=( B U A) then by using this we can solve these
a) A ⊕ B= (A - B) U (B - A)= (B-A) U (A-B)= B⊕A
b)Let A=a∪c and B=b∪c, a is disjoint from b, a is disjoint from c
(A⊕B) ⊕B = ((a U c) ⊕ (b U c)) ⊕ ( b U c)
=(a U b) ⊕ (b U c)
=(a U c)
=A
