Asked by Jen

Determine which, if any, of the three statements are equivalent. Give a reason for your conclusion.

I) If the garden needs watering, then the garden does not need weeding.
II) Either the garden needs watering or the garden does not need weeding.
III) If the garden does not need watering, then the garden does not need weeding.

a. None are equivalent
b. I, II, and III are equivalent
c. I and II are equivalent
d. I and III are equivalent
e. II and III are equivalent

Answers

Answered by Ms. Sue
I'll be glad to comment on your answer.
Answered by Jen
I think it's b. but i'm not sure what my reasoning would be....
Answered by Ms. Sue
I disagree with your answer.

I. states that if the garden is dry, the weeds don't grow.
II. states an either/or situation -- either it's dry or the weeds don't grow.
III. states that if it's wet, then the weeds don't grow.

Answered by Max
Disregard my previous post on a similar question. I now have a better understanding.

I suggest converting each statement into symbolic form.

Let p = the garden needs watering.
Let p = the garden needs weeding.

I. p --> ~q
II. p V ~q
III. ~p --> q

Looks like the answer is a; none of them are equivalent.

Here's a side note: a statement is always logically equivalent to it's contrapositive, i.e., p --> q is equivalent to ~q --> ~p.

If I am in Paris, then I am in France.
If I am not in France, then I am not in Paris.
II.
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