Question

Assertion: The expression ~ (X ∨ Y) is logically equivalent to (~X ∧ ~Y)

Reason: The commutative property of logical operators states that the order of the operands does not change the result of a binary operation.

Options

• Both Assertion and Reason are true and Reason is the correct explanation for Assertion.

• Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.

• Assertion is true and Reason is false.

• Both Assertion and Reason are false.

Answer 1

Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.

Explanation:

The commutative property of logical operators states that changing the order of operands does not affect the result of a binary operation. However, according to De Morgan’s law, the negation of a disjunction is equal to the conjunction of the negations, that is, ∼ (A ∨ B) = (∼A ∧ ∼B). Therefore, the given Assertion is true.