Determine which, if any, of the three statements are equivalent.
-I. If the garden needs watering, then the garden needs weeding or the garden is not lovely.
II. The garden needs watering, and it is false that the garden does not need weeding and the Garden is not lovely.
III. The garden needs watering, and the garden needs weeding or the garden is lovely.
A) II and III are equivalent
B) I and III are equivalent
C) I and II are equivalent
D) None are equivalent

Question

Quizplus · Accepted Answer

II and III are equivalent when analyzed through logical equivalences. Statement II can be rewritten using De Morgan's laws and the negation of a conjunction, which makes it logically equivalent to Statement III. Both statements essentially assert that if the garden needs watering, it must either need weeding or be lovely, directly opposing the condition where it doesn't need weeding and is not lovely.

Determine Which, If Any, of the Three Statements Are Equivalent