UGC NET CSE | June 2007 | Part 2 | Question: 9

Question

If $A\oplus B=C,$ then:

• A. $A\oplus C=B$
• B. $B\oplus C=A$
• C. $A\oplus B\oplus C=1$
• D. $A\oplus B\oplus C=0$

Answer 1

Given that $A \oplus B = C$

$(A)A \oplus C \\ \equiv A \oplus(A \oplus B)\\ \equiv(A \oplus A) \oplus B\\ \equiv 0 \oplus B\\ \equiv B$

Option (A) is true.

$(B)B \oplus C \\ \equiv B \oplus(A \oplus B) \\ \equiv B \oplus ( B \oplus A)\\ \equiv (B \oplus B )\oplus A\\ \equiv 0 \oplus A\\ \equiv A$
Option(B)is true.

$(C)A \oplus B \oplus C \\ \equiv A \oplus B \oplus(A \oplus B) \\ \equiv A \oplus B \oplus ( B \oplus A)\\ \equiv A \oplus(B \oplus B )\oplus A\\ \equiv A \oplus 0 \oplus A\\ \equiv A \oplus A\\ \equiv 0$

Option(C)is false.

(D)from (C) option(D) is true.

 
Hence,Option(A),(B) and (D)are true.

Answer 2

Option D is correct.

Putting the value of A $\oplus$ B in option D, we get C $\oplus$ C $=$ $0$