 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/discrete-mathematics-continuous-mathematics-and-probability/1/c/solution

C

to both sides, then use its associativity and the identities in (b)(i):

(A \oplus C) \oplus C = (B \oplus C) \oplus C ⟹ A \oplus (C \oplus C) = B \oplus (C \oplus C) ⟹ A \oplus \emptyset = B \oplus \emptyset .

The final identity gives $A = B$ . This is cancellation by applying the same operation twice.

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