Previous Year Question
Which one of the following is not a valid rule of Boolean algebra?
Correct answer: B
Explanation
A Boolean variable and its complement always have opposite logic values, so X is not generally equal to X̄. In contrast, standard Boolean identities include X+1=1, X·X=X and X+0=X. Thus the invalid rule is option B.
Formula
X+X̄=1; X·X̄=0; therefore X≠X̄
Step-by-step solution
Correct Answer
B — X = X̄
Concept and Reasoning
A Boolean variable and its complement always have opposite logic values, so X is not generally equal to X̄. In contrast, standard Boolean identities include X+1=1, X·X=X and X+0=X. Thus the invalid rule is option B.
Calculation / Key Relation
X+X̄=1
X·X̄=0
therefore X≠X̄
Exam Takeaway
Complement means the opposite Boolean value.
Common Mistake
Do not confuse X=X̄ with the valid complement identities.
Common mistake
Do not confuse X=X̄ with the valid complement identities.
Exam tip
Complement means the opposite Boolean value.
Quick method
Complement means the opposite Boolean value.