Answer
a) A ⊕ A= (A - A) U (A - A)= ∅ U ∅= ∅
b) A ⊕ ∅=(A - ∅ ) U (∅ - A)= A U ∅ =A
c) A ⊕ U=(A - U) U (U - A) = ∅ U A= A
d) A ⊕ A=(A - A) U (A - A)= A U A= U
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) then by using this we can solve these
a) A ⊕ A= (A - A) U (A - A)= ∅ U ∅= ∅
b) A ⊕ ∅=(A - ∅ ) U (∅ - A)= A U ∅ =A
c) A ⊕ U=(A - U) U (U - A) = ∅ U A= A
d) A ⊕ A=(A - A) U (A - A)= A U A= U
