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4 votes
4 votes

If $A\oplus B=C$, then which one of the following is true?

  1. $A\oplus C=B$
  2. $B\oplus C=A$
  3. $A\oplus B\oplus C=0$
  4. Both (A) and (B)
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2 Answers

4 votes
4 votes
Answer Option A,B and C all are correct

Possible Conditions

A⊕B=C         Option A) A⊕C=B     Option B) B⊕C=A        Option C) A⊕B⊕C=0

0⊕0=0                        0⊕0=0=B                   0⊕0=0=A                       0⊕0⊕0=0

1⊕0=1                        1⊕1=0=B                   0⊕1=1=A                       1⊕0⊕1=0

0⊕1=1                        0⊕1=1=B                   1⊕1=0=A                       1⊕0⊕1=0

1⊕1=0                        1⊕0=1=B                   1⊕0=1=A                       1⊕0⊕1=0
1 votes
1 votes
We can make a truth table and observe that, which one is true.
$${\begin{array}{|c|c|c|}\hline
A& B& C&A\oplus B &B\oplus C&A\oplus C &A\oplus B \oplus C\\\hline
{\color{Magenta} {0}}& {\color{Blue} {0}}& {\color{Red} {0}} & {\color{Red}{0} } & {\color{Magenta} {0}} & {\color{Blue} {0}} & {\color{Purple} {0}} \\\hline   
0& 0& 1&0 & 1 & 1 & 1 \\\hline 0& 1& 0&1 & 1 & 0 & 1 \\\hline
{\color{Magenta} {0}}&{\color{Blue} {1}}&{\color{Red} {1}}&{\color{Red} {1}} & {\color{Magenta} {0}}& {\color{Blue} {1}} &  {\color{Purple} {0}}\\\hline
1&0&0&1& 0 & 1 & 1 \\\hline
{\color{Magenta} {1}} &{\color{Blue} {0}}&{\color{Red} {1}}&{\color{Red} {1}} & {\color{Magenta} {1}}  & {\color{Blue} {0}} & {\color{Purple} {0}}  \\\hline
{\color{Magenta} {1}} &{\color{Blue} {1}}&{\color{Red} {0}}&{\color{Red} {0}}  & {\color{Magenta} {1}}& {\color{Blue} {1}} & {\color{Purple} {0}}   \\\hline
 1&1&1&0 & 0 & 0  & 1\\\hline
\end{array}}$$
From the above truth table, if $A\oplus B = C, $ then $A\oplus C= B,\;B\oplus C= A,\;A\oplus B \oplus C = 0.$

So, the correct answer is $(D).$
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