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Study the Assertion and Reason and choose the correct option.
A=0 B=1 C=0 and D=1 and minterm is A' · B · C' · D Which one of the following options is correct?
Assertion: $A=0\quad B=1\quad C=0$ and $D=1$ and minterm is $A' \cdot B \cdot C' \cdot D$
Reason: The final sum term must be $0$ so $A$ and $C$ are complemented.
Which one of the following options is correct?
- (a)Both Assertion and Reason are true, and Reason is the correct explanation for Assertion.
- (b)Both Assertion and Reason are true, but Reason is not the correct explanation for Assertion.
- (c)Assertion is true and Reason is false.
- (d)Assertion is false and Reason is true.
Answer
Answer
Correct option: (c)
The Assertion is true: for a minterm, a variable is written uncomplemented if its value is 1 and complemented if its value is 0; here $A=0, B=1, C=0, D=1$ gives exactly $A'BC'D$, which matches the given minterm. The Reason is false: it calls this a 'sum term' that 'must be 0', but that is the rule for forming a MAXTERM (POS) - a minterm is a PRODUCT term that must evaluate to 1, not a sum term equal to 0; so the Reason's stated justification is incorrect even though its numeric conclusion happens to agree. Answer: (c) Assertion is true and Reason is false.