Question 3102 – 2014 June UGC NET Paper 1
January 6, 2024Question 11047 – Sequential-Circuits
January 6, 2024Question 11043 – Theory-of-Computation
Which of the following expressions is equivalent to (A⊕B)⊕C
Correct Answer: C
Question 4 Explanation:
(A⊕B)⊕C
⇒ We know that
A⊕B = A’B + AB’
A⊙B = AB + A’B’
⇒ (A⊕B)’C + (A⊕B)C’
⇒ (A⊙B)C + (A’B + AB’)C’
⇒ (AB + A’B’)C + (A’B + AB’)C’
⇒ ABC + A’B’C + A’BC’ + AB’C’
⇒ ABC + (A’B’C + A’B’C) + A’BC’ + AB’C’
[We know that A + A = A]
⇒ ABC + A’B’C + A’B’C + A’BC’ + AB’C’
⇒ ABC + A'(B’C + BC’) + B'(A’C + AC’)
⇒ ABC + A'(B⊕C) + B'(A⊕C)
⇒ We know that
A⊕B = A’B + AB’
A⊙B = AB + A’B’
⇒ (A⊕B)’C + (A⊕B)C’
⇒ (A⊙B)C + (A’B + AB’)C’
⇒ (AB + A’B’)C + (A’B + AB’)C’
⇒ ABC + A’B’C + A’BC’ + AB’C’
⇒ ABC + (A’B’C + A’B’C) + A’BC’ + AB’C’
[We know that A + A = A]
⇒ ABC + A’B’C + A’B’C + A’BC’ + AB’C’
⇒ ABC + A'(B’C + BC’) + B'(A’C + AC’)
⇒ ABC + A'(B⊕C) + B'(A⊕C)
None of these
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