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Study the Assertion and Reason and choose the correct option.
The expression ~ ( X ∨ Y ) is logically equivalent to (~ X ∧ ~ Y) Given below are two statements…
Assertion: The expression $\sim ( X \vee Y )$ is logically equivalent to $(\sim X \wedge \sim Y)$
Reason: The commutative property of logical operators states that the order of the operands does not change the result of a binary operation.
Given below are two statements marked, Assertion and Reason. Read the two statements carefully and choose the correct option.
- (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)Both Assertion and Reason are false.
Answer
Answer
Correct option: (b)
Answer: (b) Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.
Assertion: $\sim(X \vee Y) = (\sim X \wedge \sim Y)$ is true, by De Morgan's law. Reason: the commutative property (order of operands does not change the result of a binary operation) is also a true statement, but it is unrelated to De Morgan's law and does not explain why the Assertion holds.