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Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Digital-Grand Test -Q2


Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177
+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. (A \oplus B) \oplus C = A \oplus (B \oplus C )

2. (A \odot B) \odot C = A \odot (B \odot C)

3. A \oplus B \oplus C = A \odot B \odot C

4. 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

asked Jun 10, 2020 by gbeditor-2 (72,840 points)
reshown Jun 12, 2020 by gbeditor-2

1 Answer

0 votes
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)
Answer:

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177
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