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# Digital-Grand Test -Q2

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+1 vote

Let A,B,C be three boolean variables. $\oplus$ and $\odot$ are exclusive-or(ExOr) and exclusive-nor(ExNor) operations respectively.

Consider the following  statements :

1. $\dpi{100} (A \oplus B) \oplus C = A \oplus (B \oplus C )$

2. $\dpi{100} (A \odot B) \odot C = A \odot (B \odot C)$

3. $\dpi{100} A \oplus B \oplus C = A \odot B \odot C$

4. $\dpi{100} A \oplus B \oplus C = \overline{( A \odot B \odot C )}$

Which of the above statements is/are correct ?

(A). 1 and 3 only

(B). 2 and 4 only

(C). 1,2 and 3 only

(D). 1,2 and 4 only

reshown Jun 12, 2020

1 and 2 are obviously correct as xor and xnor are associative

3 is also correct as LHS = (A'B+AB')C'+(A'B+AB')'C =A'BC'+AB'C'+ABC+A'B'C

RHS = (AB+A'B')C+ (AB+A'B')'C'=ABC+A'B'C+A'BC'+AB'C' =LHS

hence c is correct
answered Jun 21, 2020 by (18,750 points)